Related papers: 1D Potts, Yang-Lee Edges and Chaos
We prove that for the Ising model on a lattice of dimensionality $d \ge 2$, the zeros of the partition function $Z$ in the complex $\mu$ plane (where $\mu=e^{-2\beta H}$) lie on the unit circle $|\mu|=1$ for a wider range of $K_{n n'}=\beta…
We study the $q$-state Potts models on a cubic lattice in the thermodynamic limit using tensor renormalization group transformations with the triad approximation. By computing the thermodynamic potentials, we locate the first-order phase…
We discuss the q-state Potts models for q<=4, in the scaling regimes close to their critical or tricritical points. Starting from the kink S-matrix elements proposed by Chim and Zamolodchikov, the bootstrap is closed for the scaling regions…
The surface and bulk properties of the two-dimensional Q > 4 state Potts model in the vicinity of the first order bulk transition point have been studied by exact calculations and by density matrix renormalization group techniques. For the…
Hysteresis is studied in a disordered Ising model in which diffusion of antiferromagnetic bonds is allowed in addition to spin flips. Saturation behavior changes to a figure-eight loop when diffusion is introduced. The upper and lower…
In statistical physics, one of the standard methods to study second order phase transitions is the renormalization group that usually leads to an expansion around the corresponding fully connected solution. Unfortunately, often in…
We introduce a new way of reconstructing the equation of state of a thermodynamic system near a second order critical point from a finite set of Taylor coefficients computed away from the critical point. We focus on the Ising universality…
The three-dimensional $q$-state Potts model, forced into coexistence by fixing the density of one state, is studied for $q=2$, 3, 4, and 6. As a function of temperature and number of states, we studied the resulting equilibrium droplet…
We reconsider Ising spins in a Gaussian random field within the replica formalism. The corresponding continuum model involves several coupling constants beyond the single one which was considered in the standard $\phi^4$ theory approach.…
We performed Monte Carlo simulations of two-dimensional $q$-state Potts models with $q=10,15$, and $20$ and measured the spin-spin correlation function at the first-order transition point $\beta_t$ in the disordered and ordered phase. Our…
Matter exhibits phases and their transitions. These transitions are classified as first-order phase transitions (FOPTs) and continuous ones. While the latter has a well-established theory of the renormalization group, the former is only…
A rigorous theorem due to Aizenman and Wehr asserts that there can be no latent heat heat in a two-dimensional system with quenched random impurities. We examine this result, and its possible extensions to higher dimensions, in the context…
The peculiar phase-ordering properties of a lattice of coupled chaotic maps studied recently (A. Lema\^\i tre & H. Chat\'e, {\em Phys. Rev. Lett.} {\bf 82}, 1140 (1999)) are revisited with the help of detailed investigations of interface…
We find the cross-over behavior for the spin-spin correlation function for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation approach of the perturbation series…
We classify four-state spin models with interactions along the edges according to their behavior under a specific group of symmetry transformations. This analysis uses the measure of complexity of the action of the symmetries, in the spirit…
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…
The critical behaviour in short time dynamics for the q=6 and 7 state Potts models in two-dimensions is investigated. It is shown that dynamic finite-size scaling exists for first-order phase transitions.
We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find…
The infinite-volume limit behavior of the 2d Ising model under possibly strong random boundary conditions is studied. The model exhibits chaotic size-dependence at low temperatures and we prove that the `+' and `-' phases are the only…
We establish an intriguing connection between geometry and thermodynamics in the critical q-state Potts model on two-dimensional lattices, using the q-state bond-correlated percolation model (QBCPM) representation. We find that the number…