Related papers: On $p$-state $p$-adic Potts model on a Cayley tree

We evaluate the thermodynamic properties of the 4-state antiferromagnetic Potts model on the Union- Jack lattice using tensor-based numerical methods. We present strong evidence for a previously unknown, "entropy-driven," finite-temperature…

We examine the behavior of the sequences of $p$-adic valuations of quadratic polynomials with integer coefficients for an odd prime $p$ through tree representations. Under this representation, a finite tree corresponds to a periodic…

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…

We determine reductions of 2-dimensional, irreducible, semi-stable, and non-crystalline representations of $\mathrm{Gal}(\overline{\mathbb Q}_p/\mathbb Q_p)$ with Hodge--Tate weights $0 < k-1$ and with $\mathcal L$-invariant whose $p$-adic…

The study of prime divisibility plays a crucial role in number theory. The $p$-adic valuation of a number is the highest power of a prime, $p$, that divides that number. Using this valuation, we construct $p$-adic valuation trees to…

A $p$-adic version of Gromov-Witten invariants for counting plane curves of genus $g$ and degree $d$ through a given number of points is discussed. The multiloop version of $p$-adic string theory considered by Chekhov and others motivates…

We study $p$-adic manifolds associated with twisted points of quotient stacks $\mathcal{X} = [U/G]$ and their quotient spaces $\pi:\mathcal{X} \to X$. We prove several structural results about the fibres of $\pi$ and derive in particular a…

We construct a p-adic Eisenstein measure with values in the space of vector-weight p-adic automorphic forms on certain unitary groups. This measure allows us to p-adically interpolate special values of certain vector-weight C-infinity…

The stable profile of the boundary of a plant's leaf fluctuating in the direction transversal to the leaf's surface is described in the framework of a model called a "surface \`a godets". It is shown that the information on the profile is…

We consider irreversible translation-invariant interacting particle systems on the $d$-dimensional cubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy…

We construct the exact partition function of the Potts model on a complete graph subject to external fields with linear and nematic type couplings. The partition function is obtained as a solution to a linear diffusion equation and the free…

We study images of equilibrium (Gibbs) states for a class of non-invertible transformations associated to conformal iterated function systems with overlaps $\mathcal S$. We prove exact dimensionality for these image measures, and find a…

We study the relative entropy density for generalized Gibbs measures. We first show its existence and obtain a familiar expression in terms of entropy and relative energy for a class of ``almost Gibbsian measures'' (almost sure continuity…

We consider the Curie-Weiss Potts model in zero external field under independent symmetric spin-flip dynamics. We investigate dynamical Gibbs-non-Gibbs transitions for a range of initial inverse temperatures beta<3, which covers the phase…

We study the interfacial adsorption phenomena of the three-state ferromagnetic Potts model on the simple cubic lattice by the Monte Carlo method. Finite-size scaling analyses of the net-adsorption yield the evidence of the phase transition…

In this work, we model the temperature measurement as a transformation of the arbitrary state into the Gibbs state. We start with a general formalism of ansatz-posteriors, which includes many usual models of posterior states due to…

Let $Z_n(z,t)$ denote the partition function of the $q$-state Potts Model on the rooted binary Cayley tree of depth~$n$. Here, $z = {\rm e}^{-h/T}$ and $t = {\rm e}^{-J/T}$ with $h$ denoting an externally applied magnetic field, $T$ the…

In this paper, building upon ideas of Naor and Tao and continuing the study initiated in by the authors and Safe, sufficient conditions are provided for weighted weak type and strong type $(p,p)$ estimates with $p>1$ for the centered…

This paper provides unified calculations regarding certain measures and transformations in interacting particle systems. More specifically, we provide certain general conditions under which an interacting particle system will have a…

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.…