Related papers: Transfer matrix computation of critical polynomial…
We present exact solutions for the zero-temperature partition function (chromatic polynomial $P$) and the ground state degeneracy per site $W$ (= exponent of the ground-state entropy) for the $q$-state Potts antiferromagnet on strips of the…
We study the effect of interfacial phenomena in two-dimensional perfect and random (or disordered) $q$-state Potts models with continuous phase transitions, using, mainly, Monte Carlo techniques. In particular, for the total interfacial…
For the $q$-state Potts model on a Cayley tree of order $k\geq 2$ it is well-known that at sufficiently low temperatures there are at least $q+1$ translation-invariant Gibbs measures which are also tree-indexed Markov chains. Such measures…
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…
We calculate complex-temperature (CT) zeros of the partition function for the $q$-state Potts model on the honeycomb and kagom\'e lattices for several values of $q$. These give information on the CT phase diagrams. A comparison of results…
The critical points of the 3-states two-layer Potts model on square lattice for different interlayer couplings (Kx, Ky,and Kz) are calculated with high precision using probabilistic cellular automata with Glauber algorithm, where Kx and Ky…
We analyze a three-state Potts model built over a lattice ring, with coupling $J_0$, and the fully connected graph, with coupling $J$. This model is effectively mean-field and can be exactly solved by using transfer-matrix method and…
We propose an iterative proposal to estimate critical points for statistical models based on configurations by combing machine-learning tools. Firstly, phase scenarios and preliminary boundaries of phases are obtained by…
The Potts model is one of the most popular spin models of statistical physics. The prevailing majority of work done so far corresponds to the lattice version of the model. However, many natural or man-made systems are much better described…
Let $M_d$ be the moduli space of one-dimensional complex polynomial dynamical systems. The escape rates of the critical points determine a critical heights map $G: M_d \to \mathbb{R}^{d-1}$. For generic values of $G$, each connected…
In previous work, it has been shown that the recently proposed LLR method is very efficient at overcoming strong metastabilities that arise near first-order phase transition points. Here we present a systematic study of the performance of…
A mapping is developed between the quantum Hall plateau transition and two-dimensional self-interacting lattice polymers. This mapping is exact in the classical percolation limit of the plateau transition, and diffusive behavior at the…
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 investigate the ferromagnetic $q$-state Potts model on spherical Fibonacci graphs. These graphs are constructed by embedding quasi-uniform sites on a sphere and defining interactions via a chord-distance cutoff chosen to yield a network…
Let f be a degree d polynomial defined over the nonarchimedean field C_p, normalized so f is monic and f(0)=0. We say f is post-critically bounded, or PCB, if all of its critical points have bounded orbit under iteration of f. It is known…
The vicinity of the critical point of the three-state Potts model on a Kagom\'e lattice is studied by mean of Random Matrix Theory. Strong evidence that the critical point is integrable is given.
Let $p(z)$ be a monic cubic complex polynomial with distinct roots and distinct critical points. We say a critical point has the {\it Voronoi property} if it lies in the Voronoi cell of a root $\theta$, $V(\theta)$, i.e. the set of points…
Since its introduction, the Potts model has gained widespread popularity across various fields due to its diverse applications. Even minor advancements in this model continue to captivate scientists worldwide, and small modifications often…
We derive exact relations between the Potts model partition function, or equivalently the Tutte polynomial, for a network (graph) $G$ and a network obtained from $G$ by (i) by replacing each edge (i.e., bond) of $G$ by two or more edges…
In the QCD phase diagram, the dependence of the pseudo-critical temperature, $T_{\rm{pc}}$, on the baryon chemical potential, $\mu_B$, is of fundamental interest. The variation of $T_{\rm{pc}}$ with $\mu_B$ is normally captured by $\kappa$,…