Related papers: Antiferromagnetic Potts Models on the Square Latti…
In this paper we present an extensive study of the thermodynamic properties of the two-dimensional quantum Heisenberg antiferromagnet on the square lattice; the problem is tackled by the pure-quantum self-consistent harmonic approximation,…
We study the finite temperature (FT) phase transitions of two-dimensional (2D) $q$-states Potts models on the square lattice, using the first principles Monte Carlo (MC) simulations as well as the techniques of neural networks (NN). We…
Here we consider a one-dimensional $q$-state Potts model with an external magnetic field and an anisotropic interaction that selects neighboring sites that are in the spin state 1. The present model exhibits an unusual behavior in the…
The S=1/2 and S=1 two-dimensional quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice are investigated by the quantum Monte Carlo method. By finite-size-scaling analyses on the correlation lengths, the…
We present exact solutions for the zero-temperature partition function of the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial $P$) on tube sections of the simple cubic lattice of fixed transverse size $L_x \times…
We present a quantum Monte Carlo study of a Heisenberg antiferromagnet on a spatially anisotropic square lattice, where the coupling strength in the x-direction ($J_x$) is different from that in the y-direction ($J_y$). By varying the…
We obtain the exact scale invariant scattering solutions for two-dimensional field theories with replicated permutational symmetry $\mathbb{S}_q$. After sending to zero the number of replicas they correspond to the renormalization group…
In this paper we study the phase diagram of the five-state Potts antiferromagnet on the bisected-hexagonal lattice. This question is important since Delfino and Tartaglia recently showed that a second-order transition in a five-state Potts…
We study the properties of the Wang-Swendsen-Kotecky cluster Monte Carlo algorithm for simulating the 3-state kagome-lattice Potts antiferromagnet at zero temperature. We prove that this algorithm is not ergodic for symmetric subsets of the…
The effect of quenched impurities on systems which undergo first-order phase transitions is studied within the framework of the q-state Potts model. For large q a mapping to the random field Ising model is introduced which provides a simple…
We consider the $q$-state Potts model on families of self-dual strip graphs $G_D$ of the square lattice of width $L_y$ and arbitrarily great length $L_x$, with periodic longitudinal boundary conditions. The general partition function $Z$…
An isotropic anti-ferromagnetic quantum state on a square lattice is characterized by symmetry arguments only. By construction, this quantum state is the result of an underlying valence bond structure without breaking any symmetry in the…
We present numerical results for an $S=1/2$ Heisenberg antiferromagnet on a inhomogeneous square lattice with tunable interaction between spins belonging to different plaquettes. Employing Quantum Monte Carlo, we significantly improve on…
We study the ground state degeneracy per site (exponent of the ground state entropy) $W(\Lambda,(L_x=\infty) \times L_y,q)$ for the $q$-state Potts antiferromagnet on infinitely long strips with width $L_y$ of 2D lattices $\Lambda$ with…
The zeros of the partition function of the ferromagnetic q-state Potts model with long-range interactions in the complex-q plane are studied in the mean-field case, while preliminary numerical results are reported for the finite 1d chains…
We report the magnetic and calorimetric measurements in single crystal samples of the square lattice $J_{1}-J_{2}$ quantum antiferromagnet BaCdVO(PO$_4$)$_2$. An investigation of the scaling of magnetization reveals a "dimensionality…
We study using Monte Carlo simulations the finite-size scaling behavior of the interfacial adsorption of the two-dimensional square-lattice $q$-states Potts model. We consider the pure and random-bond versions of the Potts model for $q =…
The Q-state Potts model can be extended to noninteger and even complex Q in the FK representation. In the FK representation the partition function,Z(Q,a), is a polynomial in Q and v=a-1(a=e^-T) and the coefficients of this…
We continue our discussion of the q-state Potts models for q <= 4, in the scaling regimes close to their critical and tricritical points. In a previous paper, the spectrum and full S-matrix of the models on an infinite line were elucidated;…
In this paper, we study the annealed ferromagnetic $q$-state Potts model on sparse rank-1 random graphs, where vertices are equipped with a vertex weight, and the probability of an edge is proportional to the product of the vertex weights.…