Retracted: New Mathematical Conception and Computation Algorithm for Study of Quantum 3D Disordered Spin System under the Influence of External Field

2010 ◽  
pp. E1-E1
Author(s):  
Ashot S. Gevorkyan ◽  
Chin-Kun Hu ◽  
Sergei Flach
Keyword(s):  
External Field ◽  
Spin System ◽  
Computation Algorithm ◽  
Mathematical Conception

scholarly journals Contraction: A Unified Perspective of Correlation Decay and Zero-Freeness of 2-Spin Systems

2021 ◽  
Vol 185 (2) ◽  
Author(s):  
Shuai Shao ◽  
Yuxin Sun
Keyword(s):  
Partition Function ◽  
Approximation Algorithms ◽  
External Field ◽  
Spin System ◽  
Spin Systems ◽  
Interaction Parameters ◽  
Entire Family ◽  
Bounded Degree ◽  
Correlation Decay ◽  
Complex Valued

AbstractWe study the connection between the correlation decay property (more precisely, strong spatial mixing) and the zero-freeness of the partition function of 2-spin systems on graphs of bounded degree. We show that for 2-spin systems on an entire family of graphs of a given bounded degree, the contraction property that ensures correlation decay exists for certain real parameters implies the zero-freeness of the partition function and the existence of correlation decay for some corresponding complex neighborhoods. Based on this connection, we are able to extend any real parameter of which the 2-spin system on graphs of bounded degree exhibits correlation decay to its complex neighborhood where the partition function is zero-free and correlation decay still exists. We give new zero-free regions in which the edge interaction parameters and the uniform external field are all complex-valued, and we show the existence of correlation decay for such complex regions. As a consequence, we obtain approximation algorithms for computing the partition function of 2-spin systems on graphs of bounded degree for these complex parameter settings.

scholarly journals A complexity classification of spin systems with an external field

2015 ◽  
Vol 112 (43) ◽  
pp. 13161-13166 ◽  
Author(s):  
Leslie Ann Goldberg ◽  
Mark Jerrum
Keyword(s):  
Ising Model ◽  
External Field ◽  
Spin System ◽  
Spin Systems ◽  
Ferromagnetic Ising Model ◽  
Complexity Classification ◽  
Antiferromagnetic Ising Model ◽  
Computational Difficulty ◽  
State Spin

We study the computational complexity of approximating the partition function of a q-state spin system with an external field. There are just three possible levels of computational difficulty, depending on the interaction strengths between adjacent spins: (i) efficiently exactly computable, (ii) equivalent to the ferromagnetic Ising model, and (iii) equivalent to the antiferromagnetic Ising model. Thus, every nontrivial q-state spin system, irrespective of the number q of spins, is computationally equivalent to one of two fundamental two-state spin systems.

scholarly journals TWO-DIMENSIONAL LATTICE GRAVITY AS A SPIN SYSTEM

1994 ◽  
Vol 05 (02) ◽  
pp. 359-361 ◽  
Author(s):  
W. BEIRL ◽  
H. MARKUM ◽  
J. RIEDLER
Keyword(s):  
Partition Function ◽  
External Field ◽  
Path Integral ◽  
Spin System ◽  
Higher Dimensions ◽  
Two Dimensional ◽  
Path Integral Formulation ◽  
Regge Calculus ◽  
Dimensional Lattice ◽  
Matter Fields

Quantum gravity is studied in the path integral formulation applying the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin system with higher couplings on a Kagomé lattice. Various measures acting as external field are considered. Extensions to matter fields and higher dimensions are discussed.

scholarly journals Stochastic resonance of an Ising spin system driven by stochastic external field

2004 ◽  
Vol 53 (9) ◽  
pp. 3157
Author(s):  
Shao Yuan-Zhi ◽  
Zhong Wei-Rong ◽  
Lin Guang-Ming ◽  
Li Jian-Can
Keyword(s):  
External Field ◽  
Stochastic Resonance ◽  
Spin System ◽  
Ising Spin ◽  
Ising Spin System

scholarly journals Resilience of networks with community structure behaves as if under an external field

2018 ◽  
Vol 115 (27) ◽  
pp. 6911-6915 ◽  
Author(s):  
Gaogao Dong ◽  
Jingfang Fan ◽  
Louis M. Shekhtman ◽  
Saray Shai ◽  
Ruijin Du ◽  
...  
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Community Structure ◽  
External Field ◽  
Spin System ◽  
Real World ◽  
Percolation Theory ◽  
Universality Class ◽  
Networked Systems ◽  
Scaling Relations

Although detecting and characterizing community structure is key in the study of networked systems, we still do not understand how community structure affects systemic resilience and stability. We use percolation theory to develop a framework for studying the resilience of networks with a community structure. We find both analytically and numerically that interlinks (the connections among communities) affect the percolation phase transition in a way similar to an external field in a ferromagnetic– paramagnetic spin system. We also study universality class by defining the analogous critical exponents δ and γ, and we find that their values in various models and in real-world coauthor networks follow the fundamental scaling relations found in physical phase transitions. The methodology and results presented here facilitate the study of network resilience and also provide a way to understand phase transitions under external fields.

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