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The surface and bulk properties of the two-dimensional Q > 4 state Potts model in the vicinity of the first order bulk transition point have been studied by exact calculations and by density matrix renormalization group techniques. For the…

Statistical Mechanics · Physics 2009-10-31 Ferenc Igloi , Enrico Carlon

We study the critical behavior of the q-state Potts model with random ferromagnetic couplings. Working with the cluster representation the partition sum of the model in the large-q limit is dominated by a single graph, the fractal…

Disordered Systems and Neural Networks · Physics 2009-11-07 Robert Juhasz , Heiko Rieger , Ferenc Igloi

We develop a variational wave function for the ground state of a one-dimensional bosonic lattice gas. The variational theory is initally developed for the quantum rotor model and later on extended to the Bose-Hubbard model. This theory is…

Condensed Matter · Physics 2009-11-10 J. J. Garcia-Ripoll , J. I. Cirac , P. Zoller , C. Kollath , U. Schollwoeck , J. von Delft

We prove a recent conjecture on the duality relation for correlation functions of the Potts model for boundary spins of a planar lattice. Specifically, we deduce the explicit expression for the duality of the n-site correlation functions,…

Statistical Mechanics · Physics 2009-10-30 Wentao T. Lu , F. Y. Wu

The study of ground-state properties of the Fermi-Hubbard model is a long-lasting task in the research of strongly correlated systems. Owing to the exponentially growing complexity of the system, a quantitative analysis usually demands high…

Strongly Correlated Electrons · Physics 2023-08-15 Yue-Ran Shi , Yuan-Yao He , Ruijin Liu , Wei Zhang

We present an exact solution of the q-state Potts model on a class of generalized Sierpinski fractal lattices. The model is shown to possess an ordered phase at low temperatures and a continuous transition to the high temperature disordered…

Disordered Systems and Neural Networks · Physics 2015-06-15 Liang Tian , Hui Ma , Wenan Guo , Lei-Han Tang

A new duality relation is derived for the Potts model in one dimension. It is shown that the partition function is self-dual with the nearest-neighbor interaction and the external field appearing as dual parameters. Zeroes of the partition…

Statistical Mechanics · Physics 2007-05-23 F. Y. Wu

The Potts conformal field theory is an analytic continuation in the central charge of conformal field theory describing the critical two-dimensional $Q$-state Potts model. Four-point functions of the Potts conformal field theory are…

High Energy Physics - Theory · Physics 2023-06-14 Rongvoram Nivesvivat

We develop a systematic method of obtaining duality symmetric actions in different dimensions. This technique is applied for the quantum mechanical harmonic oscillator, the scalar field theory in two dimensions and the Maxwell theory in…

High Energy Physics - Theory · Physics 2007-05-23 R. Banerjee , C. Wotzasek

We applied the simulated tempering and magnetizing (STM) method to the two-dimensional three-state Potts model in an external magnetic field in order to perform further investigations of the STM's applicability. The temperature as well as…

Statistical Mechanics · Physics 2014-05-16 Tetsuro Nagai , Yuko Okamoto , Wolfhard Janke

The q-state Potts model on a diamond chain has mathematical significance in analyzing phase transitions and critical behaviors in diverse fields, including statistical physics, condensed matter physics, and materials science. By focusing on…

Statistical Mechanics · Physics 2023-10-30 Yury Panov , Onofre Rojas

It is known rigorously that the phase transition of the $q$-state ferromagnetic Potts model on the square lattice is second order for $q=4$. Despite this fact, some observables of the $q=4$ model show features of a first-order phase…

Statistical Mechanics · Physics 2025-03-18 Yuan-Heng Tseng , Shang-Wei Li , Fu-Jiun Jiang

We have calculated the large-$q$ expansion for the energy and magnetization cumulants at the first order phase transition point in the two-dimensional $q$-state Potts model to the 21st or 23rd order in $1/\sqrt{q}$ using the finite lattice…

High Energy Physics - Lattice · Physics 2009-10-31 H. Arisue , K. Tabata

We discover an Ising-type duality in the general $N$-state chiral Potts model, which is the Kramers-Wannier duality of planar Ising model when N=2. This duality relates the spectrum and eigenvectors of one chiral Potts model at a low…

Statistical Mechanics · Physics 2010-01-13 Shi-shyr Roan

Second-order variational type equations for spatial point processes are established. In case of log linear parametric models for pair correlation functions, it is demonstrated that the variational equations can be applied to construct…

We consider q-state Potts models coupled by their energy operators. Restricting our study to self-dual couplings, numerical simulations demonstrate the existence of non-trivial fixed points for 2 <= q <= 4. These fixed points were first…

Statistical Mechanics · Physics 2009-10-31 Vladimir Dotsenko , Jesper Lykke Jacobsen , Marc-Andre Lewis , Marco Picco

We present results of a numerical simulation of the 3-state Potts model with random bond, in two dimension. In particular, we measure the critical exponent associated to the magnetization and the specific heat. We also compare these…

Condensed Matter · Physics 2009-10-28 Marco Picco

The partition function of the q-state Potts model with random ferromagnetic couplings in the large-q limit is generally dominated by the contribution of a single diagram of the high temperature expansion. Computing this dominant diagram…

Statistical Mechanics · Physics 2007-05-23 J-Ch. Angles d'Auriac , F. Igloi , M. Preissmann , A. Sebo

In this paper, we show analytically that the duality of normal factor graphs (NFG) can facilitate stochastic estimation of partition functions. In particular, our analysis suggests that for the $q-$ary two-dimensional nearest-neighbor Potts…

Information Theory · Computer Science 2014-01-29 Ali Al-Bashabsheh , Yongyi Mao

Gauging and duality transformations, two of the most useful tools in many-body physics, are shown to be equivalent up to constant depth quantum circuits in the case of one-dimensional quantum lattice models. This is demonstrated by making…