Recently gigantic peaks in thermodynamic response functions have been observed at finite temperature for one-dimensional models with short-range coupling, closely resembling a second-order phase transition. Thus, we will analyze the finite temperature pseudo-transition property observed in some one-dimensional models and its relationship with finite size effect. In particular, we consider two chain models to study the finite size effects; these are the Ising-Heisenberg tetrahedral chain and an Ising-Heisenberg-type ladder model. Although the anomalous peaks of these one-dimensional models have already been studied in the thermodynamic limit, here we will discuss the finite size effects of the chain and why the peaks do not diverge in the thermodynamic limit. So, we discuss the dependence of the finite size effects, for moderately and sufficiently large systems, in which the specific heat and magnetic susceptibility exhibit peculiar rounded towering peaks for a given temperature. This behavior is quite similar to a continuous phase transition, but there is no singularity. For moderately large systems, the peaks narrow and increase in height as the number of unit cells is increased, and the location of peak shifts slightly. Hence, one can naively induce that the sharp peak should lead to a divergence in the thermodynamic limit. However, for a rather large system, the height of a peak goes asymptotically to a finite value. Our result confirms the dependence of the peak height with the number of unit cells at the pseudo-critical temperature. We also provide an alternative empirical function that satisfactorily fits specific heat and magnetic susceptibility at pseudo-critical temperature. Certainly, our result is crucial to understand the finite size correction behavior in quantum spin models, which in general are only numerically tractable within the framework of the finite size analysis.
We construct and analyse a dual model to the Ising model with the nearest and next-nearest neighbors on the rectangular lattice (NNNI model). The Hamiltonian of the dual model turns out to contain two- and four-spin interactions. The free fermion approximation suggests that an increase in the critical temperature of the dual model caused by the four-spin interactions is limited to a finite range.
We study the dependence of complex-temperature phase diagrams on details of the Hamiltonian, focusing on the effect of non-nearest-neighbor spin-spin couplings. For this purpose, we consider a simple exactly solvable model, the 1D Ising model with nearest-neighbor (NN) and next-to-nearest-neighbor (NNN) couplings. We work out the exact phase diagrams for various values of $J_{nnn}/J_{nn}$ and compare these with the case of pure nearest-neighbor (NN) couplings. We also give some similar results for the 1D Potts model with NN and NNN couplings.
We study the collapse transition of a polymer on a square lattice with both nearest-neighbor and next nearest-neighbor interactions, by calculating the exact partition function zeros up to chain length 36. The transition behavior is much more pronounced than that of the model with nearest-neighbor interactions only. The crossover exponent and the transition temperature are estimated from the scaling behavior of the first zeros with increasing chain length. The results suggest that the model is of the same universality class as the usual theta point described by the model with only nearest-neig…
The second neighbor correlation functions of the spin-${1/2}$ $XXZ$ chain in the ground state are expressed in the form of three dimensional integrals. We show that these integrals can be reduced to one-dimensional ones and thereby evaluate the values of the next nearest-neighbor correlation functions for ${Δ>1}$.
The level-spacing distributions of XXZ spin chains with next-nearest-neighbor couplings are studied under periodic boundary conditions. We confirm that integrable XXZ spin chains mostly have the Poisson distribution as expected. On the contrary, the level-spacing distributions of next-nearest-neighbor coupled XXZ chains are given by non-Wigner distributions. It is against the expectations, since the models are nonintegrable.
We consider a fermionic Hubbard chain with an additional next-to-nearest neighbor hopping term. We study the thermalization rates of the quasi-momentum distribution function within a quantum Boltzmann equation approach. We find that the thermalization rates are proportional to the square of the next-to-nearest neighbor hopping: Even weak next-to-nearest neighbor hopping in addition to nearest neighbor hopping leads to thermalization in a two-particle scattering quantum Boltzmann equation in one dimension. We also investigate the temperature dependence of the thermalization rates, which away fr…
We study phase transitions and thermodynamic properties in the two-dimensional antiferromagnetic Ising model with next-nearest-neighbor interaction on a Kagome lattice by Monte Carlo simulations. A histogram data analysis shows that a second order transition occurs in the model. From the analysis of obtained data, we can assume that next-nearest-neighbor ferromagnetic interactions in two-dimensional antiferromagnetic Ising model on a Kagome lattice excite the occurrence of a second order transition and unusual behavior of thermodynamic properties on the temperature dependence.
The axial next-nearest-neighbor Ising model is studied in two dimensions at finite temperature using the density matrix renormalization group. The model exhibits phase transition of the second-order between the antiphase in low temperature and the modulated phase in high temperature. Observing the domain wall free energy, we confirm that the modulation period in high-temperature side is well explained by the free-fermion picture.
A model for cooperative sequential adsorption that incorporates nearest-neighbor exclusion and next-nearest neighbor interaction is presented. It is analyzed for the case of one-dimensional dimer and two-dimensional monomer adsorption. Analytic solutions found for certain values of the interaction strength are used to investigate jamming coverage and temporal approach to jamming in the one-dimensional case. In two dimensions, the series expansion of the coverage $θ(t)$ is presented and employed to provide estimates for the jamming coverage as a function of interaction strength. These estimates…
The critical and multicritical behavior of the simple cubic Ising model with nearest-neighbor, next-nearest-neighbor and plaquette interactions is studied using the cube and star-cube approximations of the cluster variation method and the recently proposed cluster variation--Padé approximant method. Particular attention is paid to the line of critical end points of the ferromagnetic-paramagnetic phase transition: its (multi)critical exponents are calculated, and their values suggest that the transition belongs to a novel universality class. A rough estimate of the crossover exponent is also gi…
We consider the model of strongly-correlated system of electrons described by an extended Falicov-Kimball Hamiltonian where the stability of some axial and diagonal striped phases was proved. Introducing a next-nearest-neighbor hopping, small enough not to destroy the striped structure, we examine rigorously how the presence of the next-nearest-neighbor hopping anisotropy reduces the $π/2$-rotation degeneracy of the diagonal-striped phase. The effect appears to be similar to that in the case of anisotropy of the nearest-neighbor hopping: the stripes are oriented in the direction of the weaker …
The mean field theory of a spin glass with a specific form of nearest and next nearest neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we either find the continuous replica symmetry breaking seen in the Sherrington-Kirkpartick model or a one step solution similar to that found in structural glasses. Our results are confirmed by numerical simulations and the link between the type of spin-glass behavior and the density of eigenvalues of the interaction matrix is discussed.
An $S=1/2$ triangular-lattice Heisenberg antiferromagnet with next-nearest-neighbor interactions is investigated under a magnetic field by the numerical-diagonalization method. It is known that, in both cases of weak and strong next-nearest-neighbor interactions, this system reveals a magnetization plateau at one-third of the saturated magnetization. We examine the stability of this magnetization plateau when the amplitude of next-nearest-neighbor interactions is varied. We find that a nonplateau region appears between the plateau phases in the cases of weak and strong next-nearest-neighbor in…
Using the parallel tempering algorithm and GPU accelerated techniques, we have performed large-scale Monte Carlo simulations of the Ising model on a square lattice with antiferromagnetic (repulsive) nearest-neighbor(NN) and next-nearest-neighbor(NNN) interactions of the same strength and subject to a uniform magnetic field. Both transitions from the (2x1) and row-shifted (2x2) ordered phases to the paramagnetic phase are continuous. From our data analysis, reentrance behavior of the (2x1) critical line and a bicritical point which separates the two ordered phases at T=0 are confirmed. Based on…
We present a study of site and bond percolation on periodic lattices with 3 nearest neighbors per site. We have considered 3 lattices, with different symmetries, different underlying Bravais lattices, and different degrees of longer-range connections. As expected, we find that the site and bond percolation thresholds in all of the 3-connected lattices studied here are significantly higher than in diamond. Interestingly, thresholds for different lattices are similar to within a few percent, despite the differences between the lattices at scales beyond nearest and next-nearest neighbors.
We develop a simple technique for calculation of next to nearest neighbor spin-spin and chiral-spin correlation functions in inhomogeneous XXX model. Exact expression of the chiral-spin order parameter as a function of the model parameter, $ω$, is analytically found. Using the same method we also calculate the next to nearest neighbor spin-spin correlation function. In the limit $ω-> 0$ it reproduces the known result for the vacuum expectation value of the next to nearest neighbor spins in the standard Heisenberg spin chain. The technique is simple and can be extended for calculation of next t…
A complete classification is given for one dimensional chains with nearest neighbor interactions having two states in each site, for which a matrix product ground state exists. The Hamiltonians and their corresponding matrix product ground states are explicitly obtained.
The purpose of this note is to connect early work on thermal transport in spin-1/2 Heisenberg chains with uniaxial exchange anisotropy and nearest-neighbor interactions that was based on a moment analysis of the Fourier transform of the energy density correlation function with subsequent studies that make use of thermal current correlation functions.
The equilibrium properties of the lattice fluid with the repulsion between the nearest neighbors on the two-level planar triangular lattice are investigated. The numerical results obtained from the analytical expressions are compared with the Monte Carlo simulation data. It is shown that the previously proposed diagrammatic approximation makes it possible to determine the equilibrium characteristics of the lattice fluid with the repulsion between the nearest neighbors on a two-level lattice with an accuracy comparable to the accuracy of modelling the system using the Monte Carlo method in the …
The stationary points of the potential energy function of the ϕ^4 model on a two-dimensional square lattice with nearest-neighbor interactions are studied by means of two numerical methods: a numerical homotopy continuation method and a globally-convergent Newton-Raphson method. We analyze the properties of the stationary points, in particular with respect to a number of quantities that have been conjectured to display signatures of the thermodynamic phase transition of the model. Although no such signatures are found for the nearest-neighbor ϕ^4 model, our study illustrates the strengths and …
We introduce a fully frustrated XY model with nearest neighbor (nn) and next nearest neighbor (nnn) couplings which can be realized in Josephson junction arrays. We study the phase diagram for $0\leq x \leq 1$ ($x$ is the ratio between nnn and nn couplings). When $x < 1/\sqrt{2}$ an Ising and a Berezinskii-Kosterlitz-Thouless transitions are present. Both critical temperatures decrease with increasing $x$. For $x > 1/\sqrt{2}$ the array undergoes a sequence of two transitions. On raising the temperature first the two sublattices decouple from each other and then, at higher temperatures, each s…
We study a random neighbor version of the Bak-Sneppen model, where "nearest neighbors" are chosen according to a probability distribution decaying as a power-law of the distance from the active site, P(x) \sim |x-x_{ac }|^{-ω}. All the exponents characterizing the self-organized critical state of this model depend on the exponent ω. As ωtends to 1 we recover the usual random nearest neighbor version of the model. The pattern of results obtained for a range of values of ωis also compatible with the results of simulations of the original BS model in high dimensions. Moreover, our results suggest…
The single-particle spectral properties near the Mott transition in the two-dimensional Hubbard model with next-nearest-neighbor hopping are investigated by using cluster perturbation theory. Complicated spectral features of this model are simply interpreted, by considering how the next-nearest-neighbor hopping shifts the spectral weights of the two-dimensional Hubbard model. Various anomalous features observed in hole-doped and electron-doped cuprate high-temperature superconductors are explained in a unified manner as properties near the Mott transition in a two-dimensional system whose spec…
As is well known, one-dimensional systems with interactions restricted to first nearest neighbors admit a full analytically exact statistical-mechanical solution. This is essentially due to the fact that the knowledge of the first nearest-neighbor probability distribution function, $p_1(r)$, is enough to determine the structural and thermodynamic properties of the system. On the other hand, if the interaction between second nearest-neighbor particles is turned on, the analytically exact solution is lost. Not only the knowledge of $p_1(r)$ is not sufficient anymore, but even its determination b…
In the paper random-site percolation thresholds for simple cubic lattice with sites' neighborhoods containing next-next-next-nearest neighbors (4NN) are evaluated with Monte Carlo simulations. A recently proposed algorithm with low sampling for percolation thresholds estimation [Bastas et al., arXiv:1411.5834] is implemented for the studies of the top-bottom wrapping probability. The obtained percolation thresholds are $p_C(\text{4NN})=0.31160(12)$, $p_C(\text{4NN+NN})=0.15040(12)$, $p_C(\text{4NN+2NN})=0.15950(12)$, $p_C(\text{4NN+3NN})=0.20490(12)$, $p_C(\text{4NN+2NN+NN})=0.11440(12)$, $p_C…
