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 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.

(2, 0) SUPERSYMMETRIC STRING THEORY AND THE CRITICAL EXPONENTS OF THE 3D ISING MODEL

1991 ◽  
Vol 06 (29) ◽  
pp. 2687-2691 ◽  
Author(s):  
M. A. MOJUMDER
Keyword(s):  
Ising Model ◽  
String Theory ◽  
Excellent Agreement ◽  
Critical Exponents ◽  
World Sheet ◽  
Theoretical Results ◽  
Matter Fields ◽  
3D Ising Model

Critical exponents α and β for the 3D Ising model have been obtained by a study of partial non-renormalization of superconformal dimensions of matter fields on (2, 0) supersymmetric string world-sheet. An ansatz has been used to calculate the exact numerical values which are in excellent agreement with experimental and other theoretical results.

scholarly journals Disorder, order, and domain wall roughening in the two-dimensional random field Ising model

1998 ◽  
Vol 58 (5) ◽  
pp. R5217-R5220 ◽  
Author(s):  
E. T. Seppälä ◽  
V. Petäjä ◽  
M. J. Alava
Keyword(s):  
Ising Model ◽  
Domain Wall ◽  
Random Field ◽  
Two Dimensional ◽  
Random Field Ising Model

scholarly journals Interconversion of multiferroic domains and domain walls

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
E. Hassanpour ◽  
M. C. Weber ◽  
Y. Zemp ◽  
L. Kuerten ◽  
A. Bortis ◽  
...  
Keyword(s):  
Domain Wall ◽  
Physical Properties ◽  
Domain Walls ◽  
Three Dimensional ◽  
Topological Defects ◽  
Long Range Order ◽  
Two Dimensional ◽  
Domain Structures ◽  
Topological Singularities ◽  
Ordered State

AbstractSystems with long-range order like ferromagnetism or ferroelectricity exhibit uniform, yet differently oriented three-dimensional regions called domains that are separated by two-dimensional topological defects termed domain walls. A change of the ordered state across a domain wall can lead to local non-bulk physical properties such as enhanced conductance or the promotion of unusual phases. Although highly desirable, controlled transfer of these properties between the bulk and the spatially confined walls is usually not possible. Here, we demonstrate this crossover by confining multiferroic Dy0.7Tb0.3FeO3 domains into multiferroic domain walls at an identified location within a non-multiferroic environment. This process is fully reversible; an applied magnetic or electric field controls the transformation. Aside from expanding the concept of multiferroic order, such interconversion can be key to addressing antiferromagnetic domain structures and topological singularities.

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