For the repulsive Blume-Emery-Griffiths model the phase diagram in the space of three fields, temperature (T), crystal field ($Δ$), and magnetic field (H), is computed on a complete graph, in the canonical and microcanonical ensembles. For weak strength of the biquadratic interaction (K), there exists a tricritical point in the phase diagram where three critical lines meet. As K decreases below a threshold value(which is ensemble dependent), new multicritical points like the critical end point and bicritical end point arise in the (T,$Δ$) plane. For K>-1, we observe that the two critical lines in the H plane and the multicritical points are different in the two ensembles. At K=-1, the two critical lines in the H plane disappear and as K decreases further, there is no phase transition in the H plane. Exactly at K=-1 the two ensembles become equivalent. Beyond that for all K<-1, there are no multicritical points and there is no ensemble inequivalence in the phase diagram. We also study the transition lines in the H plane for positive K i.e. for attractive biquadratic interaction. We find that the transition lines in the H plane are not monotonic in temperature for large positive K.
Ground-state properties of the Blume-Emery-Griffiths model with antiferromagnetic nearest-neighbor interactions on a triangular lattice are investigated in the presence of an external magnetic field. In particular, we explore the model's parameter space and identify regions with different degenerate ground states that may give rise to different magnetic phases also at finite temperatures. We demonstrate the presence of such phases by Monte Carlo simulations of magnetization processes for selected values of parameters.
With the aid of Ruppeiner thermodynamic metric defined on a two-dimensional phase space of dipolar ($m$) and quadrupolar ($q$) order parameters, we derive an expression for the Ricci scalar ($R$) in the isotropic Blume-Emery-Griffiths model. Temperature dependence of $R$ is investigated for various values of bilinear to biquadratic ratio ($r$). Its behavior near the continuous/discontinuous phase transition temperatures and a tricritical point is presented. It is found that in addition to the divergence singularity and finite jumps connected with the phase transitions there are field-dependent…
I study the one-dimensional spin-1 Blume-Emery-Griffiths model with bilinear and biquadratic exchange interactions and single-ion crystal field under an applied magnetic field. This model can be exactly mapped into a tight-binding Hubbard model - extended to include intersite interactions - provided one renormalizes the chemical and the on-site potentials, which become temperature dependent. After this transformation, I provide the exact solution of the Blume-Emery-Griffiths model in one dimension by means of the Green's functions and equations of motion formalism. I investigate the magnetic v…
We present a mean field analysis of a fully frustrated Ising spin model on an Ising lattice gas. This is equivalent to a degenerate Blume-Emery-Griffiths model with frustration, which we analyze for different values of the quadrupolar interaction. This model might be useful in the study of structural glasses and related systems with disorder.
The canonical phase diagram of the Blume-Emery-Griffiths (BEG) model with infinite-range interactions is known to exhibit a fourth order critical point at some negative value of the bi-quadratic interaction $K<0$. Here we study the microcanonical phase diagram of this model for $K<0$, extending previous studies which were restricted to positive $K$. A fourth order critical point is found to exist at coupling parameters which are different from those of the canonical ensemble. The microcanonical phase diagram of the model close to the fourth order critical point is studied in detail revealing s…
We study the equilibrium and dynamical properties of a spherical version of the frustrated Blume-Emery-Griffiths model at mean field level for attractive particle-particle coupling (K>0). Beyond a second order transition line from a paramagnetic to a (replica symmetric) spin glass phase, the density-temperature phase diagram is characterized by a tricritical point from which, interestingly, a first order transition line starts with coexistence of the two phases. In the Langevin dynamics the paramagnetic/spin glass discontinuous transition line is found to be dependent on the initial density; c…
We study inequivalence of canonical and microcanonical ensembles in the mean-field Blume-Emery-Griffiths model. This generalizes previous results obtained for the Blume-Capel model. The phase diagram strongly depends on the value of the biquadratic exchange interaction K, the additional feature present in the Blume-Emery-Griffiths model. At small values of K, as for the Blume-Capel model, lines of first and second order phase transitions between a ferromagnetic and a paramagnetic phase are present, separated by a tricritical point whose location is different in the two ensembles. At higher val…
Using a real-space renormalization group procedure with no adjustable parameters, we investigate the Blume-Emery-Griffiths model on the square lattice. The formalism respects sublattice symmetry, allowing the study of both signs of K, the biquadratic exchange coupling. Our results for K>0 are compared with other renormalization group calculations and with exact results, in order to assess the magnitude of the errors introduced by our approximate calculation. The quantitative agreement is excellent; values for critical parameters differ, in some cases, by less than 1% from exact ones. For K<0, …
The ferromagnetic properties of the spin-1 BEG model on finite-size Cayley tree are investigated using the exact recursion method. The spontaneous magnetization of the system is studied in detail for different values of the reduced crystal-field interaction D/J, and it is found that there is an unusual behavior (anti-Curie temperature) when D/J>2.0. We also obtain the Curie temperature of this finite-size system. When the system size is large enough, our results will fit well with that in the thermodynamic limit.
The degenerate Blume-Emery-Griffiths (DBEG) model has recently been introduced in the study of martensitic transformation problems. This model has the same Hamiltonian as the standard Blume-Emery-Griffiths (BEG) model but, to take into account vibrational effects on the martensitic transition, it is assumed that the states S=0 have a degeneracy p (p=1 corresponds to the usual BEG model). In some materials, the transition would be better described by a disordered DBEG model; further, the inclusion of disorder in the DBEG model may be relevant in the study of shape memory alloys. From the theore…
The spin-1 Ising (BEG) model with the nearest-neighbour bilinear and biquadratic interactions and single-ion anisotropy is simulated on a cellular automaton which improved from the Creutz cellular automaton(CCA) for a simple cubic lattice. The simulations have been made for several sets of parameters $K/J$ and $D/J$ in the $-3<D/J\leq 0$ and $-1\leq K/J\leq 0$ parameter regions. The re-entrant and double re-entrant phase transitions of the BEG model are determined from the temperature variations of the thermodynamic quantities ($M$, $Q$ and $χ$). The phase diagrams characterizing phase transit…
In this paper we give a complete analysis of the phase transitions in the mean-field Blume-Emery-Griffiths lattice-spin model with respect to the canonical ensemble, showing both a second-order, continuous phase transition and a first-order, discontinuous phase transition for appropriate values of the thermodynamic parameters that define the model. These phase transitions are analyzed both in terms of the empirical measure and the spin per site by studying bifurcation phenomena of the corresponding sets of canonical equilibrium macrostates, which are defined via large deviation principles. Ana…
We study in this paper the Blume-Emery-Griffiths model in a thin film of stacked triangular lattices.The model is described by three parameters: bilinear exchange interaction between spins $J$, quadratic exchange interaction $K$ and single-ion anisotropy $D$. The spin $S\_i$ at the lattice site $i$ takes three values $(-1,0,+1)$.This model can describe the mixing phase of He-4 ($S\_i =+1,-1$) and He-3 ($S\_i =0$) at low temperatures.Using Monte Carlo simulations, we show that there exists a critical value of $D$ below (above) which the transition is of second-(first-)order.In general, the temp…
The time evolution of the extremely diluted Blume-Emery-Griffiths neural network model is studied, and a detailed equilibrium phase diagram is obtained exhibiting pattern retrieval, fluctuation retrieval and self-sustained activity phases. It is shown that saddle-point solutions associated with fluctuation overlaps slow down considerably the flow of the network states towards the retrieval fixed points. A comparison of the performance with other three-state networks is also presented.
We derive the exact Helmholtz free energy (HFE) of the standard and staggered one-dimensional Blume-Emery-Griffiths (BEG) model in the presence of an external longitudinal magnetic field. We discuss in detail the thermodynamic behavior of the ferromagnetic version of the model, which exhibits magnetic field-dependent plateaux in the $z$-component of its magnetization at low temperatures. We also study the behavior of its specific heat and entropy, both per site, at finite temperature. The degeneracy of the ground state, at $T=0$, along the lines that separate distinct phases in the phase diagr…
The Blume-Emery-Griffiths spin glass is studied by renormalization-group theory in d=3. The boundary between the ferromagnetic and paramagnetic phases has first-order and two types of second-order segments. This topology includes an inverted tricritical point, first-order transitions replacing second-order transitions as temperature is lowered. The phase diagrams show disconnected spin-glass regions, spin-glass and paramagnetic reentrances, and complete reentrance, where the spin-glass phase replaces the ferromagnet as temperature is lowered for all chemical potentials.
We illustrate a novel characterization of nonequivalent statistical mechanical ensembles using the mean-field Blume-Emery-Griffiths (BEG) model as a test model. The novel characterization takes effect at the level of the microcanonical and canonical equilibrium distributions of states. For this reason it may be viewed as a statistical characterization of nonequivalent ensembles which extends and complements the common thermodynamic characterization of nonequivalent ensembles based on nonconcave anomalies of the microcanonical entropy. By computing numerically both the microcanonical and canoni…
We study the Blume-Emery-Griffiths spin glass model in presence of an attractive coupling between real replicas, and evaluate the effective potential as a function of the density overlap. We find that there is a region, above the first order transition of the model, where metastable states with a large density overlap exist. The line where these metastable states appear should correspond to a purely dynamical transition, with a breaking of ergodicity. Differently from what happens in p-spin glasses, in this model the dynamical transition would not be the precursor of a 1-step RSB transition, b…
We study the Blume-Emery-Griffiths model in a random crystal field in two and three dimensions, through a real-space renormalization-group approach and a mean-field approximation, respectively. According to the two-dimensional renormalization-group calculation, non-symmetry-breaking first-order phase transitions are eliminated and symmetry-breaking discontinuous transitions are replaced by continuous ones, when disorder is introduced. On the other hand, the mean-field calculation predicts that first-order transitions are not eliminated by disorder, although some changes are introduced in the p…
The spin-3/2 Blume-Emery-Griffiths model on a honeycomb lattice is studied by Monte Carlo simulations with the goal to determine phase diagrams for a range of the model parameters and to investigate the nature of the phase transitions between the respective phases. For positive values of the biquadratic to bilinear interaction ratio $α$, we find two ferromagnetically ordered phases, F1 and F2, with the sublattice magnetizations (1/2,1/2) and (3/2,3/2), respectively, and our results confirm the discontinuous character of the order-disorder critical line as a function of the single-ion anisotrop…
We introduce a spherical version of the frustrated Blume-Emery-Griffiths model and solve exactly the statics and the Langevin dynamics for zero particle-particle coupling (K=0). In this case the model exhibits an equilibrium transition from a disordered to a spin glass phase which is always continuous for nonzero temperature. The same phase diagram results from the study of the dynamics. Furthermore, we notice the existence of a nonequilibrium time regime in a region of the disordered phase, characterized by aging as occurs in the spin glass phase. Due to a finite equilibration time, the syste…
The spin-1 Ising (BEG) model has been simulated using a cellular automaton (CA) algorithm improved from the Creutz cellular automaton (CCA) for a face-centered cubic (fcc) lattice. The ground state diagram ($k$, $d$) of the fcc BEG model has ferromagnetic ($F$), quadrupolar ($Q$) and staggered quadrupolar ($SQ$) ordering regions. The simulations have been made in the staggered quadrupolar region for the parameter values in the intervals $ -24\leq d=D/J<0$ and $-3\leq k=K/J\leq 0$ . The phase diagrams on the ($ kT_{C}/J$, $d$) and the ($kT_{C}/J$, $k$) planes have been obtained through $ k=-3$ …
Discontinuity in the distribution of field increments between avalanches in non-abelian random field Blume-Emery-Griffiths model with no passing violation
School of Physical Sciences, National Institute of Science Education and Research（国立科学教育与研究所物理科学学院）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）
The optimal capacity of a diluted Blume-Emery-Griffiths neural network is studied as a function of the pattern activity and the embedding stability using the Gardner entropy approach. Annealed dilution is considered, cutting some of the couplings referring to the ternary patterns themselves and some of the couplings related to the active patterns, both simultaneously (synchronous dilution) or independently (asynchronous dilution). Through the de Almeida-Thouless criterion it is found that the replica-symmetric solution is locally unstable as soon as there is dilution. The distribution of the c…
We have investigated analitycally the phase diagram of a generalized spherical version of the Blume-Emery-Griffiths model that includes ferromagnetic or antiferromagnetic spin interactions as well as quadrupole interactions in zero and nonzero magnetic field. We show that in three dimensions and zero magnetic field a regular paramagnetic-ferromagnetic (PM-FM) or a paramagnetic-antiferromagnetic (PM-AFM) phase transition occurs whenever the magnetic spin interactions dominate over the quadrupole interactions. However, when spin and quadrupole interactions are important, there appears a reentran…
Renormalization group on hierarchical lattices is often considered a valuable tool to understand the critical behavior of more complicated statistical mechanical models. In presence of quenched disorder, however, in many model cases predictions obtained with the Migdal-Kadanoff bond removal approach fail to quantitatively and qualitatively reproduce critical properties obtained in the mean-field approximation or by numerical simulations in finite dimensions. In order to critically review this limitation we analyze the behavior of Ising and Blume-Emery-Griffiths models on more complicated hiera…
The Blume-Emery-Griffiths model with a random crystal field is studied in a random graph architecture, in which the average connectivity is a controllable parameter. The disordered average over the graph realizations is treated by replica symmetry formalism of order parameter functions. A self-consistent equation for the distribution of local fields is derived and numerically solved by a population dynamics algorithm. The results show that the average connectivity amounts to changes in the topology of the phase diagrams. Phase diagrams for representative values of the model parameters are comp…
We study the spin-1 Ising model with bilinear and biquadratic exchange interactions and single-ion crystal field. In addition to the four usual phases: disordered DIS, ferromagnetic FER, antiquadrupolar AQU and ferrimagnetic FRI, we found three new phases in the case of a thin magnetic film, namely: the sublattice A non magnetic phase NMA, the sublattice B non magnetic phase NMB and the global non magnetic phase NMG. These phases are studied, for each layer of the film, either in the temperature-crystal field plane $(T,Δ)$ or in the biquadratic coupling-crystal field plane $(d,Δ)$, for diferen…
The parallel dynamics of the fully connected Blume-Emery-Griffiths neural network model is studied for arbitrary temperature. By employing a probabilistic signal-to-noise approach, a recursive scheme is found determining the time evolution of the distribution of the local fields and, hence, the evolution of the order parameters. A comparison of this approach is made with the generating functional method, allowing to calculate any physical relevant quantity as a function of time. Explicit analytic formula are given in both methods for the first few time steps of the dynamics. Up to the third ti…
A generalised integer S Ising spin glass model is analysed using the replica formalism. The bilinear couplings are assumed to have a Gaussian distribution with ferromagnetic mean <J_ij> = Jo. Incorporation of a quadrupolar interaction term and a chemical potential leads to a richer phase diagram with transitions of first and second order. The first order transition may be interpreted as a phase separation, and contrary to what has been argued previously, it persists in the presence of disorder. Finally, the stability of the replica symmetric solution with respect to fluctuations in replica spa…
The Blume-Emery-Griffiths model with the dipol-quadrupol interaction (\ell) has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton (CCA) on the face centered cubic (fcc) lattice. The finite-size scaling relations and the power laws of the order parameter (M) and the susceptibility (χ) are proposed for the dipol-quadrupol interaction (\ell). The dipol-quadrupol critical exponent δ_{\ell} has been estimated from the data of the order parameter (M) and the susceptibility (χ). The simulations have been done in the interval 0\leq \ell =L/J\leq 0.01 for d…
The study of the mean-field static solution of the Random Blume-Emery-Griffiths-Capel model, an Ising-spin lattice gas with quenched random magnetic interaction, is performed. The model exhibits a paramagnetic phase, described by a stable Replica Symmetric solution. When the temperature is decreased or the density increases, the system undergoes a phase transition to a Full Replica Symmetry Breaking spin-glass phase. The nature of the transition can be either of the second order (like in the Sherrington-Kirkpatrick model) or, at temperature below a given critical value, of the first order in t…
We extend the Blume-Emery-Griffiths (BEG) model to a two-component BEG model in order to study 2D systems with two order parameters, such as magnetic superconductors or two-component Bose-Einstein condensates. The model is investigated using Monte Carlo simulations, and the temperature-concentration phase diagram is determined in the presence and absence of an external magnetic field. This model exhibits a rich phase diagram, including a second-order transition to a phase where superconductivity and magnetism coexist. Results are compared with experiments on Cerium-based heavy-fermion supercon…
In the 70's Schelling introduced a multi-agent model to describe the segregation dynamics that may occur with individuals having only weak preferences for 'similar' neighbors. Recently variants of this model have been discussed, in particular, with emphasis on the links with statistical physics models. Whereas these models consider a fixed number of agents moving on a lattice, here we present a version allowing for exchanges with an external reservoir of agents. The density of agents is controlled by a parameter which can be viewed as measuring the attractiveness of the city-lattice. This mode…
The short- and long-time dynamics of model systems undergoing a glass transition with apparent inversion of Kauzmann and dynamical arrest glass transition lines is investigated. These models belong to the class of the spherical mean-field approximation of a spin-$1$ model with $p$-body quenched disordered interaction, with $p>2$, termed spherical Blume-Emery-Griffiths models. Depending on temperature and chemical potential the system is found in a paramagnetic or in a glassy phase and the transition between these phases can be of a different nature. In specific regions of the phase diagram coe…
In ferromagnetic spin models above the critical temperature ($T > T_{cr}$) the partition function zeros accumulate at complex values of the magnetic field ($H_E$) with a universal behavior for the density of zeros $ρ(H) \sim | H - H_E |^{\sg}$. The critical exponent $\sg$ is believed to be universal at each space dimension and it is related to the magnetic scaling exponent $y_h$ via $\sg = (d-y_h)/y_h$. In two dimensions we have $y_h=12/5 (\sg = -1/6)$ while $y_h=2 (\sg=-1/2)$ in $d=1$. For the one dimensional Blume-Capel and Blume-Emery-Griffiths models we show here, for different temperature…
The Blume-Emery-Griffiths model on hypercubic lattices within the two-particle cluster approximation is investigated. The expressions for the pair correlation functions in $\bf{k}$-space are derived. On the basis of obtained results (at $\bf{k}=0$) the static susceptibility of this model on the simple cubic lattice is calculated at various values of the single-ion anisotropy and biquadratic interaction.
The simulated tempering (ST) is an important method to deal with systems whose phase spaces are hard to sample ergodically. However, it uses accepting probabilities weights which often demand involving and time consuming calculations. Here it is shown that such weights are quite accurately obtained from the largest eigenvalue of the transfer matrix -- a quantity straightforward to compute from direct Monte Carlo simulations -- thus simplifying the algorithm implementation. As tests, different systems are considered, namely, Ising, Blume-Capel, Blume-Emery-Griffiths and Bell-Lavis liquid water …
We continue our study of the thermodynamic geometry of the spin one model from paper I by probing the state space geometry of the Blume Emery Griffiths (BEG) model, and its limiting case of the Blume Capel model, in their mean field approximation. By accounting for the stochastic variables involved we construct from the thermodynamic state space two complimentary two-dimensional geometries with curvatures $R_m$ and $R_q$ which are shown to encode correlations in the model's two order parameters, namely, the magnetization $m$ and the quadrupole moment $q$. The geometry is investigated in the ze…
We study the global phase diagram of the infinite range Blume-Emery-Griffiths model both in the canonical and in the microcanonical ensembles. The canonical phase diagram is known to exhibit first order and continuous transition lines separated by a tricritical point. We find that below the tricritical point, when the canonical transition is first order, the phase diagrams of the two ensembles disagree. In this region the microcanonical ensemble exhibits energy ranges with negative specific heat and temperature jumps at transition energies. These results can be extended to weakly decaying noni…
We investigate the phase diagram of a spin--1 Ising spin-glass model on a Cayley tree. According to early work of Thompson and collaborators, this problem can be formulated in terms of a set of nonlinear discrete recursion relations along the branches of the tree. Physically relevant solutions correspond to the attractors of these mapping equations. In the limit of infinite coordination of the tree, and for some choices of the model parameters, we make contact with findings for the phase diagram of more recently investigated versions of the Blume-Emery-Griffiths spin-glass model. In addition t…
Ensemble inequivalence has been observed in several systems. In particular it has been recently shown that negative specific heat can arise in the microcanonical ensemble in the thermodynamic limit for systems with long-range interactions. We display a connection between such behaviour and a mean-field like structure of the partition function. Since short-range models cannot display this kind of behaviour, this strongly suggests that such systems are necessarily non-mean field in the sense indicated here. We illustrate our results showing an application to the Blume-Emery-Griffiths model. We f…
We develop a transfer matrix method to compute exactly the spin-spin correlation functions of Bethe lattice spin models in the external magnetic field h and for any temperature T. We first compute the correlation function for the most general spin - S Ising model, which contains all possible single-ion and nearest-neighbor pair interactions. This general spin - S Ising model includes the spin-1/2 simple Ising model and the Blume-Emery-Griffiths (BEG) model as special cases. From the spin-spin correlation functions, we obtain functions of correlation length for the simple Ising model and BEG mo…
We show here for the one-dimensional spin-1/2 ANNNI (axial-next-to-nearest-neighbor-Ising) model in an external magnetic field that the linear density of Yang-Lee zeros may diverge with critical exponent $σ= -2/3$ at the Yang-Lee edge singularity. The necessary condition for this unusual behavior is the triple degeneracy of the transfer matrix eigenvalues. If this condition is absent we have the usual value $σ= -1/2$. Analogous results have been found in the literature in the spin-1 Blume-Emery-Griffths model and in the three-state Potts model in a magnetic field with two complex components. O…
The ground state and magnetization process of the mixed spin-(1,1/2) Ising diamond chain is exactly solved by employing the generalized decoration-iteration mapping transformation and the transfer-matrix method. The decoration-iteration transformation is first used in order to establish a rigorous mapping equivalence with the corresponding spin-1 Blume-Emery-Griffiths chain in a non-zero magnetic field, which is subsequently exactly treated within the framework of the transfer-matrix technique. It is shown that the ground-state phase diagram includes just four different ground states and the l…
The phase diagram of adsorbate-induced row-type-alignments, such as missing-row reconstructions induced by adsorbate-atoms on the FCC(110) surface, is calculated by the Blume-Emmery-Griffiths (BEG) model. In the model, we introduce adatom-adatom and dipole-dipole interactions between nearest-neighbor (NN) and next-nearest-neighbor (NNN) rows. The calculation of the temperature versus adatom chemical potential phase diagram is performed using mean-field approximation. It is indicated that when NN and NNN interactions are competitive, there appear either dipole or coverage modulated (incommensur…
We propose an efficient procedure for determining phase diagrams of systems that are described by spin models. It consists of combining cluster algorithms with the method proposed by Sauerwein and de Oliveira where the grand canonical potential is obtained directly from the Monte Carlo simulation, without the necessity of performing numerical integrations. The cluster algorithm presented in this paper eliminates metastability in first order phase transitions allowing us to locate precisely the first-order transitions lines. We also produce a different technique for calculating the thermodynami…
We study the one-dimensional S=1 Blume-Emery-Griffiths model. Upon transforming the spin model into an equivalent fermionic model, we provide the exact solution within the Green's function and equations of motion formalism. We show that the relevant response functions as well as thermodynamic quantities can be determined, in the whole parameters space, in terms of a finite set of local correlators. Furthermore, considering the case of an antiferromagnetic chain with single-ion anisotropy in the presence of an external magnetic field, we find three plateaus in the magnetization curve; in the ne…
Mean-field models, while they can be cast into an {\it extensive} thermodynamic formalism, are inherently {\it non additive}. This is the basic feature which leads to {\it ensemble inequivalence} in these models. In this paper we study the global phase diagram of the infinite range Blume-Emery-Griffiths model both in the {\it canonical} and in the {\it microcanonical} ensembles. The microcanonical solution is obtained both by direct state counting and by the application of large deviation theory. The canonical phase diagram has first order and continuous transition lines separated by a tricrit…
We derive probabilistic limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume-Emery-Griffiths model. These probabilistic limit theorems consist of scaling limits for the total spin and moderate deviation principles (MDPs) for the total spin. The model under study is defined by a probability distribution that depends on the parameters $n$, $β$, and $K$, which represent, respectively, the number of spins, the inverse temperature, and the interaction strength. The intricate structure of the phase transitions is revealed by the existence o…
The order of a phase transition is usually determined by the nature of the symmetry breaking at the phase transition point and the dimension of the model under consideration. For instance, q-state Potts models in two dimensions display a second order, continuous transition for q = 2,3,4 and first order for higher q. Tamura et al recently introduced Potts models with "invisible" states which contribute to the entropy but not the internal energy and noted that adding such invisible states could transmute continuous transitions into first order transitions. This was observed both in a Bragg-Willi…
Using transfer matrix and finite-size scaling methods, we study the thermodynamic behavior of a lattice gas with two kinds of particles on the square lattice. Only excluded volume interactions are considered, so that the model is athermal. Large particles exclude the site they occupy and its four first neighbors, while small particles exclude only their site. Two thermodynamic phases are found: a disordered phase where large particles occupy both sublattices with the same probability and an ordered phase where one of the two sublattices is preferentially occupied by them. The transition betwee…
