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Related papers: Two-Dimensional Critical Potts and its Tricritical…

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Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it…

Strongly Correlated Electrons · Physics 2021-11-11 Shuo Liu , E. W. Carlson , K. A. Dahmen

Renormalization group and Coulomb gas mappings are used to derive theoretical predictions for the corrections to the exactly known asymptotic fractal masses of the hull, external perimeter, singly connected bonds and total mass of the…

Statistical Mechanics · Physics 2016-11-23 A. Aharony , J. Asikainen

We derive the exact actions of the $Q$-state Potts model valid on any graph, first for the spin degrees of freedom, and second for the Fortuin-Kasteleyn clusters. In both cases the field is a traceless $Q$-component scalar field…

High Energy Physics - Theory · Physics 2024-09-20 Kay Joerg Wiese , Jesper Lykke Jacobsen

We study the geometric properties of a system initially in equilibrium at a critical point that is suddenly quenched to another critical point and subsequently evolves towards the new equilibrium state. We focus on the bidimensional Ising…

Statistical Mechanics · Physics 2014-07-17 Thibault Blanchard , Leticia F. Cugliandolo , Marco Picco

The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters…

Statistical Mechanics · Physics 2009-11-07 Santo Fortunato

We discuss the critical behaviour of 2D Ising and q-states Potts models coupled by their energy density. We found new tricritical points. The procedure employed is the renormalisation approach of the perturbations series around conformal…

Statistical Mechanics · Physics 2009-10-30 P. Simon

We investigate the percolation behavior of Fortuin-Kasteleyn--type clusters in the spin-$1/2$ Baxter--Wu model with three-spin interactions on a triangular lattice. The considered clusters are constructed by randomly freezing one of the…

Statistical Mechanics · Physics 2026-01-23 Alexandros Vasilopoulos , Michail Akritidis , Nikolaos G. Fytas , Martin Weigel

A spin system is studied, with simultaneous permutation-symmetric Potts and spin-rotation-symmetric clock interactions, in spatial dimensions d=2 and 3. The global phase diagram is calculated from the renormalizaton-group solution with the…

Statistical Mechanics · Physics 2023-09-12 E. Can Artun , A. Nihat Berker

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

Dynamical behavior of the clusters during relaxation is studied in two-dimensional Potts model using cluster algorithm. Average cluster size and cluster formation velocity are calculated on two different lattice sizes for different number…

High Energy Physics - Lattice · Physics 2015-06-25 Yigit Gunduc , Meral Aydin

Fortuin-Kastelyn clusters in the critical $Q$-state Potts model are conformally invariant fractals. We obtain simulation results for the fractal dimension of the complete and external (accessible) hulls for Q=1, 2, 3, and 4, on clusters…

Statistical Mechanics · Physics 2010-03-04 David A. Adams , Leonard M. Sander , Robert M. Ziff

We identify a new scenario for dynamical phase transitions associated with time-integrated observables occurring in diffusive systems described by the macroscopic fluctuation theory. It is characterized by the pairwise meeting of first- and…

Statistical Mechanics · Physics 2023-07-19 Tal Agranov , Michael E. Cates , Robert L. Jack

The dynamics of 2d Potts models, which are temperature driven through the phase transition using updating procedures in the Glauber universality class, is investigated. We present calculations of the hysteresis for the (internal) energy and…

High Energy Physics - Lattice · Physics 2009-11-07 Alexander Velytsky , Bernd A. Berg , Urs M. Heller

An exact analytical solution of generalized three-state double-chain Potts model with multi-spin interactions which are invariant under cyclic shift of all spin values is obtained. The partition function in a finite cyclically closed strip…

Statistical Mechanics · Physics 2025-02-04 Pavel Khrapov , Grigory Skvortsov

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

We study $q=10$ and $q=200$ state Potts models on dynamical triangulated lattices and demonstrate that these models exhibit continuous phase transitions, contrary to the first order transition present on regular lattices. For $q=10$ the…

High Energy Physics - Lattice · Physics 2016-08-31 Jan Ambjorn , Gudmar Thorleifsson , Mark Wexler

The lattice spin model, with nearest neighbor ferromagnetic exchange and long range dipolar interaction, is studied by the method of time series for observables based on cluster configurations and associated partitions, such as Shannon…

Disordered Systems and Neural Networks · Physics 2009-11-10 M. Casartelli , L. Dall'Asta , E. Rastelli , S. Regina

We present measurements of the fractal dimensions associated to the geometrical clusters for Z_4 and Z_5 spin models. We also attempted to measure similar fractal dimensions for the generalised Fortuyin Kastelyn (FK) clusters in these…

Statistical Mechanics · Physics 2011-02-16 Marco Picco , Raoul Santachiara , Alberto Sicilia

We consider a reaction-diffusion model incorporating the reactions A -> 0, A -> 2A and 2A -> 3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order…

Statistical Mechanics · Physics 2009-11-13 Alastair L. Windus , Henrik Jeldtoft Jensen

For the two-dimensional Q-state Potts model at criticality, we consider Fortuin-Kasteleyn and spin clusters and study the average number N_Gamma of clusters that intersect a given contour Gamma. To leading order, N_Gamma is proportional to…

Statistical Mechanics · Physics 2014-02-26 István A. Kovács , Eren Metin Elçi , Martin Weigel , Ferenc Iglói