Critical behaviour of isotropic spin systems with long- and short-range interactions

1980 ◽  
Vol 55 (1) ◽  
pp. 59-77 ◽  
Author(s):  
Y. Yamazaki
Keyword(s):  
Short Range ◽  
Spin Systems ◽  
Critical Behaviour ◽  
Isotropic Spin

Static critical behaviors in random-spin systems with short-range interaction

1978 ◽  
Vol 56 (1) ◽  
pp. 139-148 ◽  
Author(s):  
Yoshitake Yamazaki
Keyword(s):  
Short Range ◽  
Spin Systems ◽  
Three Dimensions ◽  
Index Formula ◽  
Spin Component ◽  
Renormalization Group Theory ◽  
Short Range Interaction ◽  
Range Interaction ◽  
The Stability ◽  
Component Models

Critical behaviors in quenched random-spin systems with N-spin component are studied in the limit M → 0 of the non-random MN-component models by means of the renormalization group theory. As the static critical phenomena the stability of the fixed points is investigated and the critical exponents η[~ O(ε3); ε ≡ 4 – d], γ, α, and crossover index [Formula: see text] and the equation of state [~ O(ε)] are obtained. Within the approximation up to the order ε2, even the random-spin systems with N = 2 or 3 are unstable in the three dimensions and the pure systems are stable there.

scholarly journals Short-range Berezinskii-Kosterlitz-Thouless Phase Characterization for the q-state Clock Model

2021 ◽  
Author(s):  
Oscar Andres Negrete ◽  
Patricio Vargas ◽  
Francisco Jose Peña ◽  
Gonzalo Saravia ◽  
Eugenio Emilio Vogel
Keyword(s):  
Short Range ◽  
Nearest Neighbors ◽  
Vortex State ◽  
Spin Systems ◽  
Xy Model ◽  
Clock Model ◽  
Spin Correlations ◽  
Vortex States ◽  
Higher Temperature ◽  
Phase Characterization

Beyond the usual ferromagnetic and paramagnetic phases present in spin systems, the usual q-state clock model, presents an intermediate vortex state when the number of possible orientations q for the system is equal to 5 or larger. Such vortex states give rise to the Berezinskii-Kosterlitz-Thouless (BKT) phase present up to the XY model in the limit q→∞. Based on information theory, we present here an analysis of the classical order parameters plus new short-range parameters defined here. Thus, we show that even using the first nearest neighbors spin-spin correlations only, it is possible to distinguish the two transitions presented by this system for q greater than or equal to 5. Moreover, the appearance at relatively low temperature and disappearance of the BKT phase at a rather fix higher temperature is univocally determined by the short-range interactions recognized by the information content of classical and new parameters.

scholarly journals Isotropic Spin-Wave Theory of Short-Range Magnetic Order

1996 ◽  
Vol 76 (23) ◽  
pp. 4416-4419 ◽  
Author(s):  
Alexander Sokol ◽  
Rajiv R. P. Singh ◽  
Norbert Elstner
Keyword(s):  
Spin Wave ◽  
Short Range ◽  
Magnetic Order ◽  
Wave Theory ◽  
Range Magnetic Order ◽  
Spin Wave Theory ◽  
Isotropic Spin

Critical Exponents in Isotropic Spin Systems

1972 ◽  
Vol 6 (5) ◽  
pp. 1891-1893 ◽  
Author(s):  
Franz J. Wegner
Keyword(s):  
Critical Exponents ◽  
Spin Systems ◽  
Isotropic Spin

scholarly journals Ensemble equivalence in spin systems with short-range interactions

2011 ◽  
Vol 2011 (08) ◽  
pp. P08024 ◽  
Author(s):  
Kazutaka Takahashi ◽  
Hidetoshi Nishimori ◽  
Victor Martin-Mayor
Keyword(s):  
Short Range ◽  
Spin Systems ◽  
Ensemble Equivalence
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