(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.

A HEURISTIC STRING-THEORETIC APPROACH TO THE 3D ISING MODEL

1992 ◽  
Vol 07 (13) ◽  
pp. 1123-1127
Author(s):  
M. A. MOJUMDER ◽  
MESFIN TADASSE
Keyword(s):  
Fractal Dimension ◽  
Numerical Calculation ◽  
Ising Model ◽  
Critical Exponents ◽  
Field Theories ◽  
Theoretic Approach ◽  
Space Distance ◽  
Good Agreement ◽  
3D Ising Model ◽  
String Worldsheet

We have made a modification of a very heuristic relationship available in the literature between the parameter space distance and the embedding space distance on the string worldsheet. This modification along with the input of numerically determined values of the fractal dimension of the fermionic worldsheet and of the Wilson scaling dimensions of conventional ψ2 and ψ4-field theories enables a numerical calculation of the critical exponents α and β of the 3D Ising model. These values are in very good agreement with the experimental and other theoretical values.

A Test of Scaling Theory on the Critical Isotherm

1972 ◽  
Vol 50 (24) ◽  
pp. 3117-3122 ◽  
Author(s):  
D. D. Betts ◽  
L. Filipow
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Excellent Agreement ◽  
Critical Behavior ◽  
Critical Exponents ◽  
High Field ◽  
Two Dimensional ◽  
Amplitude Ratios ◽  
Critical Amplitude ◽  
Critical Isotherm

Using recently extended data of Sykes et al. on the high field expansion of the free energy of the two-dimensional spin-1/2 Ising model the critical behavior of the magnetization and its first six temperature derivatives are examined on the critical isotherm. The estimates of the critical exponents and the critical amplitude ratios are found to be in reasonable to excellent agreement with scaling theories.

scholarly journals Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$ c -Minimization and Precise Critical Exponents

2014 ◽  
Vol 157 (4-5) ◽  
pp. 869-914 ◽  
Author(s):  
Sheer El-Showk ◽  
Miguel F. Paulos ◽  
David Poland ◽  
Slava Rychkov ◽  
David Simmons-Duffin ◽  
...  
Keyword(s):  
Ising Model ◽  
Critical Exponents ◽  
Conformal Bootstrap ◽  
3D Ising Model

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 Hierarchical structure of physical Yukawa couplings from matter field Kähler metric

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Keiya Ishiguro ◽  
Tatsuo Kobayashi ◽  
Hajime Otsuka
Keyword(s):  
String Theory ◽  
Hierarchical Structure ◽  
Matter Field ◽  
Heterotic String ◽  
Heterotic String Theory ◽  
Kähler Metric ◽  
Yukawa Couplings ◽  
String Compactifications ◽  
Kahler Metric ◽  
Matter Fields

Abstract We study the impacts of matter field Kähler metric on physical Yukawa couplings in string compactifications. Since the Kähler metric is non-trivial in general, the kinetic mixing of matter fields opens a new avenue for realizing a hierarchical structure of physical Yukawa couplings, even when holomorphic Yukawa couplings have the trivial structure. The hierarchical Yukawa couplings are demonstrated by couplings of pure untwisted modes on toroidal orbifolds and their resolutions in the context of heterotic string theory with standard embedding. Also, we study the hierarchical couplings among untwisted and twisted modes on resolved orbifolds.

scholarly journals Line defects in the 3d Ising model

2013 ◽  
Vol 2013 (7) ◽  
Author(s):  
M. Billó ◽  
M. Caselle ◽  
D. Gaiotto ◽  
F. Gliozzi ◽  
M. Meineri ◽  
...  
Keyword(s):  
Ising Model ◽  
Line Defects ◽  
3D Ising Model

scholarly journals Clifford algebra approach of 3D Ising model

2018 ◽  
Vol 29 (1) ◽  
Author(s):  
Zhidong Zhang ◽  
Osamu Suzuki ◽  
Norman H. March
Keyword(s):  
Ising Model ◽  
Clifford Algebra ◽  
Algebra Approach ◽  
3D Ising Model
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