Domain Walls and Shape Dependence in the Two-Dimensional Ising-Model Critical Region

1983 ◽  
Vol 51 (12) ◽  
pp. 1058-1061 ◽  
Author(s):  
P. Kleban ◽  
G. Akinci
Keyword(s):  
Ising Model ◽  
Critical Region ◽  
Domain Walls ◽  
Two Dimensional ◽  
Shape Dependence

scholarly journals DOMAIN WALL RENORMALIZATION GROUP ANALYSIS OF TWO-DIMENSIONAL ISING MODEL

2009 ◽  
Vol 23 (18) ◽  
pp. 3739-3751 ◽  
Author(s):  
KEN-ICHI AOKI ◽  
TAMAO KOBAYASHI ◽  
HIROSHI TOMITA
Keyword(s):  
Renormalization Group ◽  
Ising Model ◽  
Domain Wall ◽  
Domain Walls ◽  
Group Analysis ◽  
Coarse Graining ◽  
Group Method ◽  
Two Dimensional ◽  
Renormalization Group Analysis ◽  
Renormalization Transformation

Using a recently proposed new renormalization group method (tensor renormalization group), we analyze the Ising model on the two-dimensional square lattice. For the lowest-order approximation with two-domain wall states, it realizes the idea of coarse graining of domain walls. We write down explicit analytic renormalization transformation and prove that the picture of the coarse graining of the physical domain walls does hold for all physical renormalization group flows. We solve it to get the fixed point structure and obtain the critical exponents and the critical temperature. These results are very near to the exact values. We also briefly report the improvement using four-domain wall states.

scholarly journals Critical Region for Droplet Formation in the Two-Dimensional Ising Model

2003 ◽  
Vol 242 (1-2) ◽  
pp. 137-183 ◽  
Author(s):  
Marek Biskup ◽  
Lincoln Chayes ◽  
Roman Kotecký
Keyword(s):  
Ising Model ◽  
Critical Region ◽  
Droplet Formation ◽  
Two Dimensional

scholarly journals Toward a 3d Ising model with a weakly-coupled string theory dual

2020 ◽  
Vol 9 (2) ◽  
Author(s):  
Nabil Iqbal ◽  
John McGreevy
Keyword(s):  
Ising Model ◽  
String Theory ◽  
Numerical Methods ◽  
Domain Wall ◽  
Phase Structure ◽  
Domain Walls ◽  
Two Dimensional ◽  
Spin Configuration ◽  
Weakly Coupled ◽  
3D Ising Model

It has long been expected that the 3d Ising model can be thought of as a string theory, where one interprets the domain walls that separate up spins from down spins as two-dimensional string worldsheets. The usual Ising Hamiltonian measures the area of these domain walls. This theory has string coupling of unit magnitude. We add new local terms to the Ising Hamiltonian that further weight each spin configuration by a factor depending on the genus of the corresponding domain wall, resulting in a new 3d Ising model that has a tunable bare string coupling g_sgs. We use a combination of analytical and numerical methods to analyze the phase structure of this model as g_sgs is varied. We study statistical properties of the topology of worldsheets and discuss the prospects of using this new deformation at weak string coupling to find a worldsheet description of the 3d Ising transition.

scholarly journals Phase transitions in GLSMs and defects

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ilka Brunner ◽  
Fabian Klos ◽  
Daniel Roggenkamp
Keyword(s):  
Phase Transitions ◽  
Boundary Conditions ◽  
Sigma Models ◽  
Domain Walls ◽  
Two Dimensional ◽  
Linear Sigma Models

Abstract In this paper, we construct defects (domain walls) that connect different phases of two-dimensional gauged linear sigma models (GLSMs), as well as defects that embed those phases into the GLSMs. Via their action on boundary conditions these defects give rise to functors between the D-brane categories, which respectively describe the transport of D-branes between different phases, and embed the D-brane categories of the phases into the category of D-branes of the GLSMs.

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