Related papers: The 3-State Square-Lattice Potts Antiferromagnet a…
We investigate the three-state antiferromagnetic Potts model on a simple cubic lattice with a cluster flipping Monte Carlo simulation algorithm in the temperature region below the transition into disorder at T_{c1}. We find both the well…
We prove the existence of long-range order at sufficiently low temperatures, including zero temperature, for the three-state Potts antiferromagnet on a class of quasi-transitive plane quadrangulations, including the diced lattice. More…
We study the antiferromagnetic 3-state Potts model on general (periodic) plane quadrangulations $\Gamma$. Any quadrangulation can be built from a dual pair $(G,G^*)$. Based on the duality properties of $G$, we propose a new criterion to…
We prove the ergodicity of the Wang--Swendsen--Koteck\'y (WSK) algorithm for the zero-temperature $q$-state Potts antiferromagnet on several classes of lattices on the torus. In particular, the WSK algorithm is ergodic for $q\ge 4$ on any…
The critical phenomena of two-dimensional (2D) antiferromagnetic $q$-state Potts model on the square lattice with $q=2,3,4,5$ and 6 are investigated using the technique of supervised neural network (NN). Unlike the conventional NN…
We study, using transfer-matrix methods, the partition-function zeros of the square-lattice q-state Potts antiferromagnet at zero temperature (= square-lattice chromatic polynomial) for the special boundary conditions that are obtained from…
We consider $S=1$ triangular lattice Heisenberg antiferromagnets with a strong single-ion anisotropy $D$ that dominates over the nearest-neighbour antiferromagnetic exchange $J$. In this limit of small $J/D$, we study low temperature ($T…
The three-state antiferromagnetic Potts model on the simple cubic lattice is investigated using the cluster variation method in the cube and the star-cube approximations. The broken-sublattice-symmetry phase is found to be stable in the…
We have simulated the classical Heisenberg antiferromagnet on a triangular lattice using a local Monte Carlo algorithm. The behavior of the correlation length $\xi$, the susceptibility at the ordering wavevector $\chi(\bf Q)$, and the spin…
The critical properties of the mixed ferro/antiferromagnetic q-state Potts model on the square lattice are investigated using the numerical transfer matrix technique. The transition temperature is found to be substantially lower than…
The correlation length of the square-lattice spin-1/2 Heisenberg antiferromagnet is studied in the low-temperature (asymptotic-scaling) regime. Our novel approach combines a very efficient loop cluster algorithm -- operating directly in the…
We exhibit infinite families of two-dimensional lattices (some of which are triangulations or quadrangulations of the plane) on which the q-state Potts antiferromagnet has a finite-temperature phase transition at arbitrarily large values of…
We show an exact equivalence of the free energy of the $q$-state Potts antiferromagnet on a lattice $\Lambda$ for the full temperature interval $0 \le T \le \infty$ and the free energy of the $q$-state Potts model on the dual lattice for a…
We map the ground-state ensemble of antiferromagnetic Ising model of spin-S on a triangular lattice to an interface model whose entropic fluctuations are proposed to be described by an effective Gaussian free energy, which enables us to…
We analyze the temperature dependence of the entropy of the spin-1/2 Heisenberg model on the three-dimensional simple-cubic lattice, for both the case of antiferromagnetic and ferromagnetic nearest neighbor exchange interactions. Using…
We present results from our analysis of the finite-temperature properties of the spin 1/2 $J_{1}$-$J_{2}$ Heisenberg model on a square lattice. The analysis is based on the exact diagonalization of small clusters with 16 and 20 sites…
We investigate the finite-temperature corrections to scaling in the three-state square-lattice Potts antiferromagnet, close to the critical point at T=0. Numerical diagonalization of the transfer matrix on semi-infinite strips of width $L$…
A Monte Carlo algorithm is proposed to simulate ferromagnetic q-state Potts model for any real q>0. A single update is a random sequence of disordering and deterministic moves, one for each link of the lattice. A disordering move attributes…
The scaling limit as T->0 of the antiferromagnetic three-state Potts model on the square lattice is described by the sine-Gordon quantum field theory at a specific value of the coupling. We show that the correspondence follows unambigously…
The temperature dependence of the correlation length, susceptibilities and the magnetic structure factor of the two-dimensional spin-1 square lattice quantum Heisenberg antiferromagnet are computed by the quantum Monte Carlo loop algorithm…