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Related papers: SLE in the three-state Potts model - a numerical s…

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Aiming at the study of critical phenomena in the presence of boundaries with a non-trivial shape we discuss how lattices with an adaptive lattice spacing can be implemented. Since the parameters of the Hamiltonian transform non-trivially…

Statistical Mechanics · Physics 2015-03-25 Martin Hasenbusch

The scaling limit of planar loop-erased random walks is described by a stochastic Loewner evolution with parameter kappa=2. In this note SLE(2) in the upper half-plane H minus a simply-connected compact subset K of H is studied. As a main…

Mathematical Physics · Physics 2009-11-13 Christian Hagendorf

In this paper, we provide a framework of estimates for describing 2D scaling limits by Schramm's SLE curves. In particular, we show that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a…

Mathematical Physics · Physics 2015-06-15 Antti Kemppainen , Stanislav Smirnov

The conjecture that the scaling limit of the two-dimensional self-avoiding walk (SAW) in a half plane is given by the stochastic Loewner evolution (SLE) with $\kappa=8/3$ leads to explicit predictions about the SAW. A remarkable feature of…

Probability · Mathematics 2009-11-07 Tom Kennedy

The nature of the zero temperature ordering transition in the 3D Gaussian random field Ising magnet is studied numerically, aided by scaling analyses. In the ferromagnetic phase the scaling of the roughness of the domain walls, $w\sim…

Disordered Systems and Neural Networks · Physics 2007-05-23 A. Alan Middleton , Daniel S. Fisher

SLE is a random growth process based on Loewner's equation with driving parameter a one-dimensional Brownian motion running with speed $\kappa$. This process is intimately connected with scaling limits of percolation clusters and with the…

Probability · Mathematics 2007-05-23 Steffen Rohde , Oded Schramm

We consider collections of $N$ chordal random curves obtained from a critical lattice model on a planar graph, in the limit when a fine-mesh graph approximates a simply-connected domain. We define and study candidates for such limits in…

Mathematical Physics · Physics 2019-03-26 Alex Karrila

We show that the conformally invariant boundary conditions for the three-state Potts model are exhausted by the eight known solutions. Their structure is seen to be similar to the one in a free field theory that leads to the existence of…

High Energy Physics - Theory · Physics 2009-10-31 J. Fuchs , C. Schweigert

Ground states of three-dimensional EA Ising spin glasses are calculated for sizes up to 14^3 using a combination of a genetic algorithm and cluster-exact approximation. For each realization several independent ground states are obtained.…

Disordered Systems and Neural Networks · Physics 2015-06-25 Alexander K. Hartmann

The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use recently developed mappings to graph-theoretic problems together with highly efficient…

Disordered Systems and Neural Networks · Physics 2018-03-02 Hamid Khoshbakht , Martin Weigel

We investigate the scaling properties of the spin interfaces in the Ashkin-Teller model. These interfaces are a very simple instance of lattice curves coexisting with a fluctuating degree of freedom, which renders the analytical…

Statistical Mechanics · Physics 2012-01-18 Y. Ikhlef , M. A. Rajabpour

We analyze the critical behaviour of the three-dimensional, three-state Potts model in the presence of an external ordering field. From a finite size scaling analysis on lattices of size up to 70**3 we determine the critical endpoint of the…

High Energy Physics - Lattice · Physics 2009-10-31 Frithjof Karsch , Sven Stickan

We argue that the lower bound to the barrier energy to flip an up/down spin domain embedded in a down/up spin environment for Ising spin glass is independent of the size of the system. The argument shows the existence of at least one…

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

We provide a representation for the scaling limit of the d=2 critical Ising magnetization field as a (conformal) random field using SLE (Schramm-Loewner Evolution) clusters and associated renormalized area measures. The renormalized areas…

Probability · Mathematics 2022-06-08 Federico Camia , Charles M. Newman

The five-dimensional Ising model with free boundary conditions has recently received a renewed interest in a debate concerning the finite-size scaling of the susceptibility near the critical temperature. We provide evidence in favour of the…

Statistical Mechanics · Physics 2016-09-13 P. H. Lundow , K. Markström

The development of Schramm--Loewner evolution (SLE) as the scaling limits of discrete models from statistical physics makes direct simulation of SLE an important task. The most common method, suggested by Marshall and Rohde \cite{MR05}, is…

Complex Variables · Mathematics 2013-03-18 Huy Tran

We study the order parameter probability distribution at the critical point for the three-dimensional spin-1/2 and spin-1 Ising models on the simple cubic lattice with periodic boundary conditions. The finite size scaling relation for the…

Statistical Mechanics · Physics 2009-11-11 B. Kutlu , M. Civi

The dilute A_3 model is a solvable IRF (interaction round a face) model with three local states and adjacency conditions encoded by the Dynkin diagram of the Lie algebra A_3. It can be regarded as a solvable version of an Ising model at the…

High Energy Physics - Theory · Physics 2008-02-03 Uwe Grimm , Bernard Nienhuis

In the ordered phase of the 3D Ising model, minority spin clusters are surrounded by a boundary of dual plaquettes. As the temperature is raised, these spin clusters become more numerous, and it is found that eventually their boundaries…

Statistical Mechanics · Physics 2023-05-03 Michael Grady

We discuss the q-state Potts models for q<=4, in the scaling regimes close to their critical or tricritical points. Starting from the kink S-matrix elements proposed by Chim and Zamolodchikov, the bootstrap is closed for the scaling regions…

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