SUPERIORITY OF GENERALIZED BOND-MOVING RENORMALIZATION IN STUDYING PHASE TRANSITION OF COMPLEX SPIN SYSTEMS

2013 ◽  
Vol 27 (32) ◽  
pp. 1350187
Author(s):  
CHUN-YANG WANG ◽  
WEN-XIAN YANG ◽  
HONG DU
Keyword(s):  
Phase Transition ◽  
External Field ◽  
Critical Points ◽  
Critical Exponents ◽  
Nearest Neighbor ◽  
Spin Systems ◽  
Scaling Theory ◽  
Complex Spin

The superiority of the generalized Migdal–Kadanoff bond-moving renormalization (GMKBR) method in studying phase transition of complex spin systems is revealed by a sampled application on the classical S4 model. In three different cases of nearest-neighbor, next-nearest neighbor and external field, we obtain the critical points and further calculate the critical exponents according to the scaling theory. In all the cases, it is shown that the method is of great convenience in obtaining results which are in good conformity with the previous ones.

Fourier transform heteronuclear magnetic triple resonance in complex spin systems—III

Polyhedron ◽  
1983 ◽  
Vol 2 (8) ◽  
pp. 783-790 ◽  
Author(s):  
Geoffrey T. Andrews ◽  
Ian J. Colquhoun ◽  
William McFarlane
Keyword(s):  
Fourier Transform ◽  
Spin Systems ◽  
Triple Resonance ◽  
Complex Spin

scholarly journals THOULESS NUMBER AND SPIN DIFFUSION IN QUANTUM HEISENBERG FERROMAGNETS

1993 ◽  
Vol 07 (27) ◽  
pp. 1747-1759 ◽  
Author(s):  
PETER KOPIETZ
Keyword(s):  
Spin Diffusion ◽  
Nearest Neighbor ◽  
Arbitrary Dimension ◽  
Quantum Spin ◽  
Spin Systems ◽  
Heisenberg Ferromagnet ◽  
Electronic Systems ◽  
Dimensionless Frequency ◽  
Spin Models ◽  
Quantum Spin Models

Using an analogy between the conductivity tensor of electronic systems and the spin stiffness tensor of spin systems, we introduce the concept of the Thouless number g0 and the dimensionless frequency-dependent conductance g(ω) for quantum spin models. It is shown that spin diffusion implies the vanishing of the Drude peak of g(ω), and that the spin diffusion coefficient Ds is proportional to g0. We develop a new method based the Thouless number to calculate D s , and present results for D s in the nearest-neighbor quantum Heisenberg ferromagnet at infinite temperatures for arbitrary dimension d and spin S.

scholarly journals Phase transition for loop representations of quantum spin systems on trees

2018 ◽  
Vol 59 (11) ◽  
pp. 113302 ◽  
Author(s):  
Volker Betz ◽  
Johannes Ehlert ◽  
Benjamin Lees
Keyword(s):  
Phase Transition ◽  
Quantum Spin ◽  
Spin Systems ◽  
Quantum Spin Systems

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.

Critical scaling theory of generalized phase transition and its universality

2000 ◽  
Vol 9 (6) ◽  
pp. 450-458 ◽  
Author(s):  
Cai Shao-hong ◽  
Hu Lin ◽  
Dai Ling-jiang ◽  
Ji Shi-yin ◽  
Li Jian-shi ◽  
...  
Keyword(s):  
Phase Transition ◽  
Scaling Theory ◽  
Critical Scaling

scholarly journals Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents

2009 ◽  
Vol 2009 ◽  
pp. 1-22 ◽  
Author(s):  
Edson D. Leonel
Keyword(s):  
Phase Transition ◽  
Critical Exponents ◽  
Scaling Laws ◽  
Scaling Function ◽  
Initial Conditions ◽  
Invariant Tori ◽  
Dynamical Variable ◽  
Two Dimensional ◽  
Control Parameters ◽  
Average Value

A phase transition from integrability to nonintegrability in two-dimensional Hamiltonian mappings is described and characterized in terms of scaling arguments. The mappings considered produce a mixed structure in the phase space in the sense that, depending on the combination of the control parameters and initial conditions, KAM islands which are surrounded by chaotic seas that are limited by invariant tori are observed. Some dynamical properties for the largest component of the chaotic sea are obtained and described in terms of the control parameters. The average value and the deviation of the average value for chaotic components of a dynamical variable are described in terms of scaling laws, therefore critical exponents characterizing a scaling function that describes a phase transition are obtained and then classes of universality are characterized. The three models considered are: The Fermi-Ulam accelerator model, a periodically corrugate waveguide, and variant of the standard nontwist map.

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