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We study the random connection model on hyperbolic space $\mathbb{H}^d$ in dimension $d=2,3$. Vertices of the spatial random graph are given as a Poisson point process with intensity $\lambda>0$. Upon variation of $\lambda$ there is a…

Probability · Mathematics 2025-10-14 Matthew Dickson , Markus Heydenreich

We study the quantum phase transition in the two-dimensional random Ising model in a transverse field by Monte Carlo simulations. We find results similar to those known analytically in one-dimension: the dynamical exponent is infinite and,…

Disordered Systems and Neural Networks · Physics 2016-08-31 C. Pich , A. P. Young

This article proposes a new way of deriving mean-field exponents for sufficiently spread-out Bernoulli percolation in dimensions $d>6$. We obtain an upper bound for the full-space and half-space two-point functions in the critical and…

Probability · Mathematics 2025-07-28 Hugo Duminil-Copin , Romain Panis

Recently Dantas, Oliveira and Stilck [J. Stat. Mech. (2007) P08009] studied how the one-dimensional diffusive contact process crosses over from the critical behavior of directed percolation to an effective mean field behaviour when the…

Statistical Mechanics · Physics 2008-04-28 Andreas Messer , Haye Hinrichsen

Realistic effective interparticle interactions of quantum many-body systems are widely seen as being short-range. However, the rigorous mathematical analysis of this type of model turns out to be extremely difficult, in general, with many…

Mathematical Physics · Physics 2023-10-09 J. -B. Bru , W. de Siqueira Pedra , K. Rodrigues Alves

In this study, we investigate bond percolation in networks that have the Poisson degree distribution and a nearest-neighbor degree-degree correlation. Previous numerical studies on percolation critical behaviors of degree-correlated…

Physics and Society · Physics 2022-03-14 Shogo Mizutaka , Takehisa Hasegawa

We develop a field-theoretic representation for the configurations of an interface between two ordered phases of a q-state Potts model in two dimensions, in the solid-on-solid approximation. The model resembles the field theory of directed…

Statistical Mechanics · Physics 2007-05-23 John Cardy

We determine the scaling functions describing the crossover from Ising-like critical behavior to classical critical behavior in two-dimensional systems with a variable interaction range. Since this crossover spans several decades in the…

Statistical Mechanics · Physics 2009-10-30 Erik Luijten , Henk W. J. Blöte , Kurt Binder

We study the ferromagnetic Ising model with long-range interactions in two dimensions. We first present results of a Monte Carlo study which shows that the long-range interactions dominate over the short-range ones in the intermediate…

Statistical Mechanics · Physics 2014-07-17 Thibault Blanchard , Marco Picco , M. A. Rajabpour

It is well established that the phase transition between survival and extinction in spreading models with short-range interactions is generically associated with the directed percolation (DP) universality class. In many realistic spreading…

Statistical Mechanics · Physics 2009-11-13 Hans-Karl Janssen , Olaf Stenull

In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one non-trivial length-scale in the model, analogous to the…

Statistical Mechanics · Physics 2009-10-31 M. E. J. Newman , D. J. Watts

Through the Monte Carlo simulation of the three-dimensional, three-state Potts model, which is a paradigm of finite-temperature pure gauge QCD, we study the fluctuations of generalized susceptibilities near the temperatures of external…

High Energy Physics - Lattice · Physics 2015-06-22 Xue Pan , Mingmei Xu , Yuanfang Wu

The one-dimensional kinetic contact process with parallel update is introduced and studied by the mean-field approximation and Monte Carlo (MC) simulations. Contrary to a more conventional scenario with single active phase for 1d models…

Statistical Mechanics · Physics 2015-03-17 P. N. Timonin , G. Y. Chitov

Phase diagrams and hysteresis loops were obtained by Monte Carlo simulations and a mean-field method for a simplified model of a spin-crossover material with a two-step transition between the high-spin and low-spin states. This model is a…

Materials Science · Physics 2016-03-01 P. A. Rikvold , G. Brown , S. Miyashita , C. Omand , M. Nishino

We study the crossover between the mean-field and critical behavior of the two-dimensional Bose gas throughout the fluctuation region of the Berezinskii--Kosterlitz--Thouless phase transition point. We argue that this crossover is described…

Condensed Matter · Physics 2009-11-07 Nikolay Prokof'ev , Boris Svistunov

We investigate the crossover properties of the frustrated percolation model on a two-dimensional square lattice, with asymmetric distribution of ferromagnetic and antiferromagnetic interactions. We determine the critical exponents nu, gamma…

Statistical Mechanics · Physics 2015-06-25 L. Cannavacciuolo , A. de Candia , A. Coniglio

We consider the critical behavior of two-dimensional Potts models in presence of a bond disorder in which the correlation decays as a power law. In some recent work the thermal sector of this theory was investigated by a renormalization…

Disordered Systems and Neural Networks · Physics 2024-07-19 Ivan Lecce , Marco Picco , Raoul Santachiara

Consider an independent site percolation model with parameter $p \in (0,1)$ on $\Z^d,\ d\geq 2$ where there are only nearest neighbor bonds and long range bonds of length $k$ parallel to each coordinate axis. We show that the percolation…

Probability · Mathematics 2011-05-24 Bernardo N. B. de Lima , Rémy Sanchis , Roger W. C. Silva

We study models of correlated percolation where there are constraints on the occupation of sites that mimic force-balance, i.e. for a site to be stable requires occupied neighboring sites in all four compass directions in two dimensions. We…

Disordered Systems and Neural Networks · Physics 2013-05-29 M. Jeng , J. M. Schwarz

Critical phenomena on scale-free networks with a degree distribution $p_k \sim k^{-\lambda}$ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify…

Statistical Mechanics · Physics 2025-08-29 Xuewei Zhao , Liwenying Yang , Dan Peng , Run-Ran Liu , Ming Li