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Related papers: Critical interfaces in the random-bond Potts model

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In various statistical-mechanical models the introduction of a metric onto the space of parameters (e.g. the temperature variable, $\beta$, and the external field variable, $h$, in the case of spin models) gives an alternative perspective…

Statistical Mechanics · Physics 2008-11-26 B. P. Dolan , D. A. Johnston , R. Kenna

We discuss recently generated high-temperature series expansions for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices. Using the star-graph expansion technique quenched disorder averages can…

Statistical Mechanics · Physics 2007-05-23 Meik Hellmund , Wolfhard Janke

We study the critical behavior of the 3-state Potts model, where the spins are located at the centers of the occupied squares of the deterministic Sierpinski carpet. A finite-size scaling analysis is performed from Monte Carlo simulations,…

Statistical Mechanics · Physics 2009-11-10 Pai-Yi Hsiao , Pascal Monceau

The study of the Ising model from a percolation perspective has played a significant role in the modern theory of critical phenomena. We consider the celebrated square-lattice Ising model and construct percolation clusters by placing bonds,…

Statistical Mechanics · Physics 2025-09-30 Tao Chen , Jinhong Zhu , Wei Zhong , Sheng Fang , Youjin Deng

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;…

High Energy Physics - Theory · Physics 2010-04-05 Patrick Dorey , Andrew Pocklington , Roberto Tateo

The self-dual random-bond eight-state Potts model is studied numerically through large-scale Monte Carlo simulations using the Swendsen-Wang cluster flipping algorithm. We compute bulk and surface order parameters and susceptibilities and…

Statistical Mechanics · Physics 2009-10-31 Christophe Chatelain , Bertrand Berche

In my PhD thesis I studied cooperative phenomena arise in complex systems using the methods of statistical and computational physics. The aim of my work was also to study the critical behaviour of interacting many-body systems during their…

Statistical Mechanics · Physics 2009-07-23 Márton Karsai

Correlation inequalities are presented for ferromagnetic Potts models with external field, using the random-cluster representation of Fortuin and Kasteleyn, together with the FKG inequality. These results extend and simplify earlier…

Mathematical Physics · Physics 2018-03-16 Geoffrey R. Grimmett

A family of models for fluctuating loops in a two dimensional random background is analyzed. The models are formulated as O(n) spin models with quenched inhomogeneous interactions. Using the replica method, the models are mapped to the…

Disordered Systems and Neural Networks · Physics 2009-08-03 Hirohiko Shimada

We provide a detailed analysis of the correlation length in the direction parallel to a line of modified coupling constants in the ferromagnetic Potts model on $\mathbb{Z}^d$ at temperatures $T>T_c$. We also describe how a line of weakened…

Mathematical Physics · Physics 2018-08-16 Sébastien Ott , Yvan Velenik

We consider the scaling limit of the two-dimensional $q$-state Potts model for $q\leq 4$. We use the exact scattering theory proposed by Chim and Zamolodchikov to determine the one and two-kink form factors of the energy, order and disorder…

High Energy Physics - Theory · Physics 2009-10-30 G. Delfino , J. L. Cardy

We present study of finite-size scaling and universality of crossing probabilities for the $q$-state Potts model. Crossing probabilities of the Potts model are similar ones in percolation problem. We numerically investigated scaling of…

Disordered Systems and Neural Networks · Physics 2007-05-23 O. A. Vasilyev

A Fortuin-Kasteleyn cluster on a torus is said to be of type $\{a,b\}, a,b\in\mathbb Z$, if it possible to draw a curve belonging to the cluster that winds $a$ times around the first cycle of the torus as it winds $-b$ times around the…

Statistical Mechanics · Physics 2010-11-04 Alexi Morin-Duchesne , Yvan Saint-Aubin

A number of interesting features of the ground states of quantum spin chains are analized with the help of a functional integral representation of the system's equilibrium states. Methods of general applicability are introduced in the…

Condensed Matter · Physics 2009-10-22 Michael Aizenman , Bruno Nachtergaele

We investigate the critical properties of the spin-3/2 Blume-Capel model in two dimensions on a random lattice with quenched connectivity disorder. The disordered system is simulated by applying the cluster hybrid Monte Carlo update…

Statistical Mechanics · Physics 2015-06-25 F. W. S. Lima , J. A. Plascak

We show how field theory yields the exact description of intermediate phases in the scaling limit of two-dimensional statistical systems at a first order phase transition point. The ability of a third phase to form an intermediate wetting…

Statistical Mechanics · Physics 2014-10-09 Gesualdo Delfino , Alessio Squarcini

The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…

Probability · Mathematics 2007-05-23 Geoffrey Grimmett

The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables,…

Statistical Mechanics · Physics 2017-09-27 M. Weigel , W. Janke

The invaded cluster approach is extended to 2D Potts model with annealed vacancies by using the random-cluster representation. Geometrical arguments are used to propose the algorithm which converges to the tricritical point in the…

Statistical Mechanics · Physics 2011-11-09 Ivan Balog , Katarina Uzelac

We prove convergence of multiple interfaces in the critical planar q = 2 random cluster model, and provide an explicit description of the scaling limit. Remarkably, the expression for the partition function of the resulting multiple…

Mathematical Physics · Physics 2020-03-20 Konstantin Izyurov