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Related papers: The six-vertex model and Schramm-Loewner evolution

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We revisit the problem of determining the Arctic curve in the six-vertex model with domain wall boundary conditions. We describe an alternative method, by which we recover the previously conjectured analytic expression in the square domain.…

Mathematical Physics · Physics 2016-11-07 Filippo Colomo , Andrea Sportiello

Based on phase space arguments, we develop a simple approach to metallic quantum critical points, designed to study the problem without integrating the fermions out of the partition function. The method is applied to the spin-fermion model…

Strongly Correlated Electrons · Physics 2009-11-07 C. Pepin , J. Rech , R. Ramazashvili

This article focuses on the characterization of global multiple Schramm-Loewner evolutions (SLE). The chordal SLE describes the scaling limit of a single interface in various critical lattice models with Dobrushin boundary conditions, and…

Probability · Mathematics 2024-08-12 Vincent Beffara , Eveliina Peltola , Hao Wu

The parametric nonlinear Schrodinger equation models a variety of parametrically forced and damped dispersive waves. For the defocusing regime, we derive a normal velocity for the evolution of curved dark-soliton fronts that represent a…

Analysis of PDEs · Mathematics 2023-08-21 Keith Promislow , Abba Ramadan

Schramm--Loewner evolution (SLE) has been one of the central topics in the probabilistic study of two-dimensional critical systems. It is a random curve in two dimensions to which a cluster interface in a critical lattice system is…

Probability · Mathematics 2025-09-03 Makoto Katori , Shinji Koshida , Chizuru Soukejima , Raian Suzuki

It is known that a backward Schramm--Loewner evolution (SLE) is coupled with a free boundary Gaussian free field (GFF) with boundary perturbation to give conformal welding of quantum surfaces. Motivated by a generalization of conformal…

Probability · Mathematics 2021-02-02 Shinji Koshida

We construct gauge theories in two extra dimensions compactified on the chiral square, which is a simple compactification that leads to chiral fermions in four dimensions. Stationarity of the action on the boundary specifies the boundary…

High Energy Physics - Phenomenology · Physics 2009-11-11 Gustavo Burdman , Bogdan A. Dobrescu , Eduardo Ponton

We study the discrete-to-continuum variational limit of the $J_{1}$-$J_{3}$ spin model on the square lattice in the vicinity of the helimagnet/ferromagnet transition point as the lattice spacing vanishes. Carrying out the…

Analysis of PDEs · Mathematics 2019-04-17 Marco Cicalese , Marwin Forster , Gianluca Orlando

The antiferromagnetic Ising model on a checkerboard lattice has an ice-like ground state manifold with extensive degeneracy. and, to leading order in J_xy, deconfined spinon excitations. We explore the role of cyclic exchange arising at…

Strongly Correlated Electrons · Physics 2007-05-23 Nic Shannon , Gregoire Misguich , Karlo Penc

We study a one-parameter family ($\ell=1,2,3,\ldots$) of configurations that are square-ice analogues of plane partitions. Using an algorithm due to Bratley and McKay, we carry out exact enumerations in order to study their asymptotic…

Statistical Mechanics · Physics 2020-01-15 Suresh Govindarajan , Anthony J. Guttmann , Varsha Subramanyan

Ice systems are prototypes of locally constrained dynamics. This is exemplified in Coulomb-liquid phases where a large space of configurations is sampled, each satisfying local ice rules. Dynamics proceeds through `flipping' rings, i.e.,…

Statistical Mechanics · Physics 2024-10-17 Adhitya Sivaramakrishnan , R. Ganesh

We analyze the free energy and the overlaps in the 2-spin spherical Sherrington Kirkpatrick spin glass model with an external field for the purpose of understanding the transition between this model and the one without an external field. We…

Disordered Systems and Neural Networks · Physics 2021-05-26 Jinho Baik , Elizabeth Collins-Woodfin , Pierre Le Doussal , Hao Wu

We apply the Tangent Method of Colomo and Sportiello to predict the arctic curves of the Twenty Vertex model with specific domain wall boundary conditions on a triangle, in the Disordered phase, leading to a phase diagram with six types of…

Mathematical Physics · Physics 2023-05-10 Philippe Di Francesco

The Green's function for the chordal Schramm-Loewner evolution $SLE_\kappa$ for $0 < \kappa < 8$, gives the normalized probability of getting near points. We give up-to-constant bounds for the two-point Green's function.

Probability · Mathematics 2015-03-29 Gregory F. Lawler , Mohammad A. Rezaei

A family of two-dimensional (2D) spin-1/2 models have been constructed to realize Kitaev's sixteen-fold way of anyon theories. Defining a one-dimensional (1D) path through all the lattice sites, and performing the Jordan-Wigner…

Strongly Correlated Electrons · Physics 2023-05-02 Jin-Tao Jin , Jian-Jian Miao , Yi Zhou

The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a…

Statistical Mechanics · Physics 2009-10-31 E. T. Seppala , V. I. Raisanen , M. J. Alava

The Shannon information-entropy uncertainty (in brief as "information uncertainty") is used to analyze the fragments in the measured 140$A$ MeV $^{40, 48}$Ca + $^{9}$Be and $^{58, 64}$Ni + $^{9}$Be reactions. A scaling phenomenon is found…

Nuclear Experiment · Physics 2016-03-23 Chun-Wang Ma , Yi-Dan Song , Chun-Yuan Qiao , Shan-Shan Wang , Hui-Ling Wei , Yu-Gang Ma , Xi-Guang Cao

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 study, we investigate the relationship between the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) equation and the stochastic Loewner equation (SLE), which is a one parameter family of the conformal mappings involving stochasticity.…

Statistical Mechanics · Physics 2026-04-07 Yusuke Kosaka Shibasaki

The scattering of a fermion in the background of a smooth step potential is considered with a general mixing of vector and scalar Lorentz structures with the scalar coupling stronger than or equal to the vector coupling. Charge-conjugation…

High Energy Physics - Theory · Physics 2015-06-19 W. M. Castilho , A. S. de Castro