A Property of Zeros of the Partition Function for Ising Spin Systems

1972 ◽  
Vol 13 (5) ◽  
pp. 781-784 ◽  
Author(s):  
Elliott H. Lieb ◽  
David Ruelle
Keyword(s):  
Partition Function ◽  
Spin Systems ◽  
Ising Spin

Entanglement in quantum dissipative Ising spin systems

2007 ◽  
Vol 398 (2) ◽  
pp. 455-459
Author(s):  
G.S. Lozano ◽  
H.F. Lozza ◽  
D. Pérez Daroca
Keyword(s):  
Spin Systems ◽  
Ising Spin

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.

PROPERTIES AND PHASE TRANSITIONS IN FRUSTRATED ISING SPIN SYSTEMS

1994 ◽  
pp. 202-237
Author(s):  
Ojiro Nagai ◽  
Tsuyoshi Horiguchi ◽  
Seiji Miyashita
Keyword(s):  
Phase Transitions ◽  
Spin Systems ◽  
Ising Spin
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