We study phases and transitions of the square-lattice double dimer model, consisting of two coupled replicas of the classical dimer model. As on the cubic lattice, we find a thermal phase transition from the Coulomb phase, a disordered but correlated dimer liquid, to a phase where fluctuations of the two replicas are closely synchronized with one another. Surprisingly, and in contrast to the cubic case, the phase boundary includes the noninteracting point, as we establish using a symmetry-based analysis of an effective height theory, indicating that infinitesimal coupling is sufficient to synchronize the double dimer model. In addition, we observe a novel antisynchronized phase when the coupling between replicas is repulsive, and use Monte Carlo simulations to establish the full phase diagram, including (anti)synchronized columnar and staggered phases, with interactions between parallel dimers in each replica.
We study a model of close-packed dimers on the square lattice with a nearest neighbor interaction between parallel dimers. This model corresponds to the classical limit of quantum dimer models [D.S. Rokhsar and S.A. Kivelson, Phys. Rev. Lett.{\bf 61}, 2376 (1988)]. By means of Monte Carlo and Transfer Matrix calculations, we show that this system undergoes a Kosterlitz-Thouless transition separating a low temperature ordered phase where dimers are aligned in columns from a high temperature critical phase with continuously varying exponents. This is understood by constructing the corresponding …
We study a generalized quantum hard-core dimer model on the square and honeycomb lattices, allowing for first and second neighbor dimers. At generalized RK points, the exact ground states can be constructed, and ground-state correlation functions can be equated to those of interacting 1+1 dimensional Grassmann fields. When the concentration of second neighbor dimers is small, the ground state correlations are shown to be short-ranged corresponding to a (gaped) spin liquid phase. On a 2-torus, the ground states exhibit fourfold topological degeneracy. On a finite cylinder we have found a dramat…
We investigate the spatially anisotropic square lattice quantum antiferromagnet. The model describes isotropic spin-1/2 Heisenberg chains (exchange constant J) coupled antiferromagnetically in the transverse (J_\perp) and diagonal (J_\times), with respect to the chain, directions. Classically, the model admits two ordered ground states -- with antiferromagnetic and ferromagnetic inter-chain spin correlations -- separated by a first order phase transition at J_\perp=2J_\times. We show that in the quantum model this transition splits into two, revealing an intermediate quantum-disordered columna…
We present a quantum Monte Carlo investigation of the finite-temperature phase diagram of the quantum dimer model on the square lattice. We use the sweeping cluster algorithm, which allows to implement exactly the dimer constraint, supplemented with a equal-time directed loop move that allows to sample winding sectors. We find a high-temperature critical phase with power-law correlations that extend down to the Rokshar-Kivelson point, in the vicinity of which a re-entrance effect in the lines of constant exponent is found. For small values of the kinetic energy strength, we find finite-tempera…
Since constraints hinder the application of numerical algorithms, phase diagrams of quantum dimer models are still controversial, even on the square lattice. The core controversy is whether the mixed state exists. In this article, we give strong evidences to solve this dispute. With our newly developed sweeping cluster method, we studied the phase diagram of large parameter space by introducing the definition of pair correlation function and other supporting evidence to distinguish the mixed phase from the columnar phase with high precision. In particular, we find that the ground state corresp…
We study spin-1/2 Heisenberg antiferromagnets on a diamond-like-decorated square lattice perturbed by two kinds of further neighbor couplings. In our previous study [J. Phys. Soc. Jpn. 85, 094002 (2016)], the second-order effective Hamiltonian for the Heisenberg model perturbed by a further neighbor coupling was found to be a square-lattice quantum-dimer model with a finite hopping amplitude, t>0, and no dimer-dimer interaction, v=0. In this study, we introduce another kind of further neighbor coupling and show that it leads to an attractive interaction between dimers, which suggests the stabi…
Using the tensor network approach, we investigate the monomer-dimer models on a checkerboard lattice, in which there are interactions (with strength $ν$) between the parallel dimers on half of the plaquettes. For the fully packed interacting dimer model, we observe a Kosterlitz-Thouless (KT) transition between the lowtemperature symmetry breaking and the high-temperature critical phases; for the doped monomer-dimer casewith finite chemical potential $μ$, we also find an order-disorder phase transition which is of second order instead. We use the boundary matrix product state approach to detect…
We study Heisenberg antiferromagnets on a diamond-like decorated square lattice perturbed by further neighbor couplings. The second-order effective Hamiltonian is calculated and the resultant Hamiltonian is found to be a square-lattice quantum-dimer model with a finite hopping amplitude and no repulsion, which suggests the stabilization of the plaquette phase. Our recipe for constructing quantum-dimer models can be adopted for other lattices and provides a route for the experimental realization of quantum-dimer models.
We present a detailed study of a model of close-packed dimers on the square lattice with an interaction between nearest-neighbor dimers. The interaction favors parallel alignment of dimers, resulting in a low-temperature crystalline phase. With large-scale Monte Carlo and Transfer Matrix calculations, we show that the crystal melts through a Kosterlitz-Thouless phase transition to give rise to a high-temperature critical phase, with algebraic decays of correlations functions with exponents that vary continuously with the temperature. We give a theoretical interpretation of these results by map…
The ground state of the square lattice bilayer quantum antiferromagnet with nearest ($J_1$) and next-nearest ($J_2$) neighbour intralayer interaction is studied by means of the dimer expansion method up to the 6-th order in the interlayer exchange coupling $J_3$. The phase boundary between the spin-gap phase and the magnetically ordered phase is determined from the poles of the biased Padé approximants for the susceptibility and the inverse energy gap assuming the universality class of the 3-dimensional classical Heisenberg model. For weak frustration, the critical interlayer coupling decrease…
We obtain a quantum dimer model (QDM) containing a Rokhsar-Kivelson (RK) point expressed by spin-1/2 Heisenberg antiferromagnets on a diamond-like decorated square lattice. This lattice has macroscopically degenerated nonmagnetic ground states, which are equivalent to the Hilbert space of a square-lattice QDM. Then, a square-lattice QDM containing the RK point as a second-order effective Hamiltonian is obtained by introducing further neighbor couplings as perturbation. Our model can provide a new method for the experimental realization of a resonating valence bond state in the QDM.
We consider a monomer-dimer system with a strong attractive dimer-dimer interaction that favors alignment. In 1979, Heilmann and Lieb conjectured that this model should exhibit a nematic liquid crystal phase, in which the dimers are mostly aligned, but do not manifest any translational order. We prove this conjecture for large dimer activity and strong interactions. The proof follows a Pirogov-Sinai scheme, in which we map the dimer model to a system of hard-core polymers whose partition function is computed using a convergent cluster expansion.
We uncover a novel mechanism for inducing a gapful phase in interacting many-body quantum chains. The mechanism is nonperturbative, being triggered only in the presence of both strong interactions and strong aperiodic (disordered) modulation. In the context of the critical antiferromagnetic spin-1/2 XXZ chain, we identify an emerging dimerization which removes the system from criticality and stabilizes the novel phase. This mechanism is shown to be quite general in strongly interacting quantum chains in the presence of strongly modulated quasiperiodic disorder which is, surprisingly, perturbat…
A mixture of hard squares, dimers and vacancies on a square lattice is known to undergo a transition from a low-density disordered phase to high-density columnar ordered phase. Along the fully packed square-dimer line, the system undergoes an Kosterliz-Thouless type transition to a phase with power law correlations. We estimate the phase boundary separating the ordered and disordered phases by calculating the interfacial tension between two differently ordered phases within two different approximation schemes. The analytically obtained phase boundary is in good agreement with Monte Carlo simul…
We present a numerical study on an interacting monomer-dimer model with nearest neighbor repulsion on a square lattice, which possesses two symmetric absorbing states. The model is observed to exhibit two nearby continuous transitions: the $Z_2$ symmetry-breaking order-disorder transition and the absorbing transition with directed percolation criticality. We find that the symmetry-breaking transition shows a non-Ising critical behavior, and that the absorbing phase becomes critical, in the sense that the critical decay of the dimer density observed at the absorbing transition persists even wit…
We study the classical hard-core dimer model on the triangular lattice. Following Kasteleyn's fundamental theorem on planar graphs, this problem is soluble by Pfaffians. This model is particularly interesting for, unlike the dimer problems on the bipartite square and hexagonal lattices, its correlations are short ranged with a correlation length of less than one lattice constant. We compute the dimer-dimer and monomer-monomer correlators, and find that the model is deconfining: the monomer-monomer correlator falls off exponentially to a constant value sin(pi/12)/sqrt(3) = .1494..., only slight…
We study a modified version of the interacting monomer-dimer (IMD) model that has infinitely many absorbing (IMA) states. Unlike all other previously studied models with IMA states, the absorbing states can be divided into two equivalent groups which are dynamically separated infinitely far apart. Monte Carlo simulations show that this model belongs to the directed Ising universality class like the ordinary IMD model with two equivalent absorbing states. This model is the first model with IMA states which does not belong to the directed percolation (DP) universality class. The DP universality …
Thermodynamic properties of the macroscopically degenerate tetramer-dimer phase of the spin-1/2 Heisenberg model on the diamond-decorated square lattice
The quantum dimer model on the square lattice is equivalent to a $U(1)$ gauge theory. Quantum Monte Carlo calculations reveal that, for values of the Rokhsar-Kivelson (RK) coupling $λ< 1$, the theory exists in a confining columnar phase. The interfaces separating distinct columnar phases display plaquette order, which, however, is not realized as a bulk phase. Static "electric" charges are confined by flux tubes that consist of multiple strands, each carrying a fractionalized flux $\frac{1}{4}$. A soft pseudo-Goldstone mode emerges around $λ\approx 0$, long before one reaches the RK point at $…
We consider a model of weakly interacting, close-packed, dimers on the two-dimensional square lattice. In a previous paper, we computed both the multipoint dimer correlations, which display non-trivial critical exponents, continuously varying with the interaction strength; and the height fluctuations, which, after proper coarse graining and rescaling, converge to the massless Gaussian field with a suitable interaction-dependent pre-factor (`amplitude'). In this paper, we prove the identity between the critical exponent of the two-point dimer correlation and the amplitude of this massless Gauss…
Loop condensed phases are scale-invariant quantum liquid phases of matter. These phases include topologically ordered liquid phases such as the toric code as well as critical liquids such as the Rokhsar-Kivelson point of the quantum dimer model on the square lattice. To investigate the extent to which nonlocal geometric observables capture a signature of the nonlocal quantum order present in these phases, we compute geometric properties of such loop condensed states using directed loop Monte Carlo calculations. In particular, we investigate the loop condensed nature of ground state of the squa…
Percolation and jamming phenomena are investigated for anisotropic sequential deposition of dimers (particles occupying two adjacent adsorption sites) on a square lattice. The influence of dimer alignment on the electrical conductivity was examined. The percolation threshold for deposition of dimers was lower than for deposition of monomers. Nevertheless, the problem belongs to the universality class of random percolation. The lowest percolation threshold (pc = 0.562) was observed for isotropic orientation of dimers. It was higher (pc = 0.586) in the case of dimers aligned strictly along one d…
We consider a classical interacting dimer model which interpolates between the square lattice case and the triangular lattice case by tuning a chemical potential in the diagonal bonds. The interaction energy simply corresponds to the number of plaquettes with parallel dimers. Using transfer matrix calculations, we find in the anisotropic triangular case a succession of different physical phases as the interaction strength is increased: a short range disordered liquid dimer phase at low interactions, then a critical phase similar to the one found for the square lattice, and finally a transition…
We study spin-1/2 Heisenberg antiferromagnets on a diamond-like-decorated square lattice. The diamond-like-decorated square lattice is a lattice in which the bonds in a square lattice are replaced with diamond units. The diamond unit has two types of antiferromagnetic exchange interactions, and the ratio $λ$ of the diagonal bond strength to that of the other four edges controls the frustration strength. For $0.974<λ<2$, the present system has a nontrivial macroscopic degeneracy, which is called the macroscopically degenerated tetramer-dimer (MDTD) states. The MDTD states are identical to the H…
We analyze classical dimer models on the square and triangular lattice using a tensor network representation of the dimers. The correlation functions are numerically calculated using the recently developed "Tensor renormalization group" (TRG) technique. The partition function for the dimer problem can be calculated exactly by the Pfaffian method which is used here as a platform for comparing the numerical results. TRG turns out to be a powerful tool for describing gapped systems with exponentially decaying correlations very efficiently due to its fast convergence. This is the case for the dime…
We show that critical exponents of the transition to columnar order in a {\em mixture} of $2 \times 1$ dimers and $2 \times 2$ hard-squares on the square lattice {\em depends on the composition of the mixture} in exactly the manner predicted by the theory of Ashkin-Teller criticality, including in the hard-square limit. This result settles the question regarding the nature of the transition in the hard-square lattice gas. It also provides the first example of a polydisperse system whose critical properties depend on composition. Our ideas also lead to some interesting predictions for a class o…
The thermodynamic properties of two-component Fermi gases with divergent scattering length is investigated and the transition temperature for the emergence of a stable dimeric gas is obtained by a simple theoretical model where the unique property of the dimers (i.e. fermionic atom pairs) with divergent scattering length is considered. Below the transition temperature, through the investigation of the overall entropy for the mixture gas of fermionic atoms and dimers, we calculate the relation between the energy and temperature of the system. In the limit of zero temperature, based on the chemi…
The monopole-dimer model introduced recently is an exactly-solvable signed generalisation of the dimer model. We show that the partition function of the monopole-dimer model on a graph invariant under a fixed-point free involution is a perfect square. We give a combinatorial interpretation of the square-root of the partition function for such graphs in terms of a monopole-dimer model on a new kind of graph with two types of edges which we call a dicot. The partition function of the latter can be written as a determinant, this time of a complex adjacency matrix. This formulation generalises T. …
We study the order-disorder transition of the two dimensional interacting monomer-dimer model (IMD) which has two symmetric absorbing states. To be self-contained, we first estimate numerically the dynamic exponent $z$ of the two dimensional Ising model. From the relaxation dynamics of the magnetization at the critical point, we obtain $β/(νz) = 0.057~650(12)$, or $z = 2.168 26(45)$, where $β= \frac{1}{8}$ and $ν=1$ are exactly known exponents. We, then, compare the critical relaxation of the order parameter at the transition point of the IMD with that of the Ising model. We found that the cri…
We present a model of classical hard-core dimers on the square lattice that contains an Ising nematic phase in its phase diagram. We consider a model with an attractive interaction for parallel dimers on a given plaquette of the square lattice and an attractive interaction for neighboring parallel dimers on the same row ({\it viz} column) of the lattice. By extensive Monte carlo simulations we find that with a finite density of holes the phase diagram has, with rising temperatures, a columnar crystalline phase, an Ising nematic liquid phase and a disordered fluid phase, separated by Ising cont…
A square-lattice hard-core dimer model with links extending beyond nearest-neighbors is studied using a directed-loop Monte Carlo method. An arbitrarily small fraction of next-nearest-neighbor dimers is found to cause deconfinement, whereas a critical state with $r^{-2}$ distance dependence of the dimer-dimer correlations persists in the presence of longer dimers preserving the bipartite graph structure. However, the critical confinement exponent governing the correlation of two test monomers is non-universal. Implications for resonating-valence-bond states are discussed.
We study a model of two-dimensional classical dimers on the square lattice with strong geometric constraints (there is exactly one bond with the nearest point for every point in the lattice). This model corresponds to the quantum dimer model suggested by D.S. Rokhsar and S.A. Kivelson (1988). We use the directed-loop algorithm to show the system undergoes a Berezinskii-Kostelitz Thousless transition (BKT transition) in finite temperatures. After that, if we destroy the geometric constraint of dimers, the topological transition will transfer to a quasi one-order transition. For the dimer update…
We discuss phase transitions and the phase diagram of a classical dimer model with anisotropic interactions defined on a square lattice. For the attractive region, the perturbation of the orientational order parameter introduced by the anisotropy causes the Berezinskii-Kosterlitz-Thouless transitions from a dimer-liquid to columnar phases. According to the discussion by Nomura and Okamoto for a quantum-spin chain system [J. Phys. A 27, 5773 (1994)], we proffer criteria to determine transition points and also universal level-splitting conditions. Subsequently, we perform numerical diagonalizati…
We propose a height-conserving quantum dimer model (hQDM) such that the lattice sum of its associated height field is conserved, and that it admits a Rokhsar-Kivelson (RK) point. The hQDM with minimal interaction range on the square lattice exhibits Hilbert space fragmentation and maps exactly to the XXZ spin model on the square lattice in certain Krylov subspaces. We obtain the ground-state phase diagram of hQDM via quantum Monte Carlo simulations, and demonstrate that a large portion of it is within the Krylov subspaces which admit the exact mapping to the XXZ model, with dimer ordered phase…
We study classical hard-core dimer models on the square lattice with links extending beyond nearest-neighbors. Numerically, using a directed-loop Monte Carlo algorithm, we find that, in the presence of longer dimers preserving the bipartite graph structure, algebraic correlations persist. While the confinement exponent for monomers drifts, the leading decay of dimer correlations remains 1/r^2, although the logarithmic peaks present in the dimer structure factor of the nearest-neighbour model vanish. By contrast, an arbitrarily small fraction of next-nearest-neighbor dimers leads to the onset o…
Covering a graph or a lattice with non-overlapping dimers is a problem that has received considerable interest in areas such as discrete mathematics, statistical physics, chemistry and materials science. Yet, the problem of percolation on dimer-covered lattices has received little attention. In particular, percolation on lattices that are fully covered by non-overlapping dimers has not evidently been considered. Here, we propose a novel procedure for generating random dimer coverings of a given lattice. We then compute the bond percolation threshold on random and ordered coverings of the squar…
We present detailed analytic calculations of finite-volume energy spectra, mean field theory, as well as a systematic low-energy effective field theory for the square lattice quantum dimer model. The analytic considerations explain why a string connecting two external static charges in the confining columnar phase fractionalizes into eight distinct strands with electric flux $\frac{1}{4}$. An emergent approximate spontaneously broken $SO(2)$ symmetry gives rise to a pseudo-Goldstone boson. Remarkably, this soft phonon-like excitation, which is massless at the Rokhsar-Kivelson (RK) point, exist…
We study the classical dimer model on a square lattice with a single vacancy by developing a graph-theoretic classification of the set of all configurations which extends the spanning tree formulation of close-packed dimers. With this formalism, we can address the question of the possible motion of the vacancy induced by dimer slidings. We find a probability 57/4-10Sqrt[2] for the vacancy to be strictly jammed in an infinite system. More generally, the size distribution of the domain accessible to the vacancy is characterized by a power law decay with exponent 9/8. On a finite system, the prob…
We show the emergence of a strongly interacting Bose-Fermi mixture from a two-component Fermi mixture with population imbalance. By analyzing in situ density profiles of $^6$Li atoms in the BCS-BEC crossover regime we identify a critical interaction strength, beyond which all minority atoms pair up with majority atoms, and form a Bose condensate. This is the regime where the system can be effectively described as a boson-fermion mixture. We determine the dimer-fermion and dimer-dimer scattering lengths and beyond-mean-field contributions. Our study realizes a Gedanken experiment of bosons imme…
Monte Carlo simulations and finite-size scaling theory have been used to study the critical behavior of repulsive dimers on square lattices at 2/3 monolayer coverage. A "zig-zag" (ZZ) ordered phase, characterized by domains of parallel ZZ strips oriented at $\pm 45^o$ from the lattice symmetry axes, was found. This ordered phase is separated from the disordered state by a order-disorder phase transition occurring at a finite critical temperature. Based on the strong axial anisotropy of the ZZ phase, an orientational order parameter has been introduced. All the critical quantities have been obt…
We study a system of interacting triplons (the elementary excitations of a valence-bond solid) described by an effective interacting boson model derived within the bond-operator formalism. In particular, we consider the square lattice spin-1/2 $J_1$-$J_2$ antiferromagnetic Heisenberg model, focus on the intermediate parameter region, where a quantum paramagnetic phase sets in, and consider the columnar valence-bond solid phase. Within the bond-operator theory, the Heisenberg model is mapped into an effective boson model in terms of triplet operators $t$. The effective boson model is studied at…
We calculate the bipartite von Neumann and second Rényi entanglement entropies of the ground states of spin-1/2 dimerized Heisenberg antiferromagnets on a square lattice. Two distinct dimerization patterns are considered: columnar and staggered. In both cases, we concentrate on the valence bond solid (VBS) phase and describe such a phase with the bond-operator representation. Within this formalism, the original spin Hamiltonian is mapped into an effective interacting boson model for the triplet excitations. We study the effective Hamiltonian at the harmonic approximation and determine the spec…
Breakdown of the thermodynamic limit in quantum spin and dimer models
Joint Quantum Institute, Department of Physics, University of Maryland（马里兰大学联合量子研究所物理系）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（马里兰大学国家标准与技术研究院联合量子信息与计算科学中心）
We consider the dimer model on the rectangular $2M \times 2N$ lattice with free boundary conditions. We derive exact expressions for the coefficients in the asymptotic expansion of the free energy in terms of the elliptic theta functions ($θ_2, θ_3, θ_4$) and the elliptic integral of second kind ($E$), up to 22nd order. Surprisingly we find that ratio of the coefficients $f_p$ in the free energy expansion for strip ($f_p^\mathrm{strip}$) and square ($f_p^\mathrm{sq}$) geometries $r_p={f_p^\mathrm{strip}}/{f_p^\mathrm{sq}}$ in the limit of large $p$ tends to $1/2$. Furthermore, we predict that …
We reassess the relation between classical lattice dimer models and the continuum elastic description of a lattice of fluctuating polymers. In the absence of randomness we determine the density and line tension of the polymers in terms of the bond weights of hard-core dimers on the square and the hexagonal lattice. For the latter, we demonstrate the equivalence of the canonical ensemble for the dimer model and the grand-canonical description for polymers by performing explicitly the continuum limit. Using this equivalence for the random bond dimer model on a square lattice, we resolve a previo…
We introduce the quantum dimer-pentamer model (QDPM) on the square lattice. This model is a generalization of the square lattice quantum dimer model as its configuration space comprises fully-packed hard-core dimer coverings as well as dimer configurations containing pentamers, where four dimers touch a vertex. Thus in the QDPM, the fully-packed, hard-core constraint of the quantum dimer model is relaxed such that the local dimer number at each vertex is fixed modulo 3, resulting in an exact local $Z_3$ gauge symmetry. We construct a local Hamiltonian for which the Rokhsar-Kivelson (RK) equal …
Two dimensional film system bears many exotic thermodynamics behaviors. We proposed a mathematical physics model to explore how the melting temperature of a two dimensional mathematical dimer film depends on the odd-eveness of the finite width of dimer film. A weak external bond between dimers is introduced into the classical dimer model in this dimer film. We derived a general equation of melting temperature and applied it for computing the melting temperature of a dimer film covering a finite square lattice. The melting temperature is proportional to the external bonding energy that we assum…
In the last few years, the methods of constructive Fermionic Renormalization Group have been successfully applied to the study of the scaling limit of several two-dimensional statistical mechanics models at the critical point, including: weakly non-integrable 2D Ising models, Ashkin-Teller, 8-Vertex, and close-packed interacting dimer models. In this note, we will focus on the illustrative example of the interacting dimer model and review some of the universality results derived in this context. In particular, we will discuss the massless Gaussian free field (GFF) behavior of the height fluctu…
The Shastry-Sutherland model --- the $S=1/2$ Heisenberg antiferromagnet on the square lattice accompanied by orthogonal dimerized interactions --- is studied by the numerical-diagonalization method. Large-scale calculations provide results for larger clusters that have not been reported yet. The present study successfully captures the phase boundary between the dimer and plaquette-singlet phases and clarifies that the spin gap increases once when the interaction forming the square lattice is increased from the boundary. Our calculations strongly suggest that in addition to the edge of the dime…
We use exact diagonalization to study the eigenstate thermalization hypothesis (ETH) in the quantum dimer model on the square and triangular lattices. Due to the nonergodicity of the local plaquette-flip dynamics, the Hilbert space, which consists of highly constrained close-packed dimer configurations, splits into sectors characterized by topological invariants. We show that this has important consequences for ETH: We find that ETH is clearly satisfied only when each topological sector is treated separately, and only for moderate ratios of the potential and kinetic terms in the Hamiltonian. B…
We have performed extensive simulations of random sequential adsorption and diffusion of $k$-mers, up to $k=5$ in two dimensions with particular attention to the case $k=2$. We focus on the behavior of the coverage and of vacancy dynamics as a function of time. We observe that for $k=2,3$ a complete coverage of the lattice is never reached, because of the existence of frozen configurations that prevent isolated vacancies in the lattice to join. From this result we argue that complete coverage is never attained for any value of $k$. The long time behavior of the coverage is not mean field and n…
Restricted-valence random sequential adsorption~(RSA) is studied in its pure and disordered versions, on the square and triangular lattices. For the simplest case~(pure on the square lattice) we prove the absence of percolation for maximum valence $V_{\rm max}=2$. In other cases, Monte Carlo simulations are used to investigate the percolation threshold, universality class, and jamming limit. Our results reveal a continuous transition for the majority of the cases studied. The percolation threshold is computed through finite-size scaling analysis of seven properties; its value increases with th…
We study the finite-size corrections of the dimer model on $\infty \times N$ square lattice with two different boundary conditions: free and periodic. We find that the finite-size corrections in a crucial way depend on the parity of $N$; we also show that such unusual finite-size behavior can be fully explained in the framework of the $c=-2$ logarithmic conformal field theory.
