Derivation of a low-temperature expansion for the general-spin Ising model

1975 ◽  
Vol 11 (1) ◽  
pp. 387-398 ◽  
Author(s):  
D. Saul ◽  
M. Ferer
Keyword(s):  
Ising Model ◽  
Low Temperature ◽  
Temperature Expansion

Low-temperature expansion in the d = 4 Ising model

1992 ◽  
Vol 374 (3) ◽  
pp. 647-666 ◽  
Author(s):  
C. Vohwinkel ◽  
P. Weisz
Keyword(s):  
Ising Model ◽  
Low Temperature ◽  
Temperature Expansion

Comment on ‘‘Low-temperature expansion for the Ising model’’

1993 ◽  
Vol 70 (5) ◽  
pp. 698-698 ◽  
Author(s):  
A. J. Guttmann ◽  
I. G. Enting
Keyword(s):  
Ising Model ◽  
Low Temperature ◽  
Temperature Expansion

scholarly journals Low temperature expansion of the gonihedric Ising model

1998 ◽  
Vol 525 (3) ◽  
pp. 549-570 ◽  
Author(s):  
R. Pietig ◽  
F.J. Wegner
Keyword(s):  
Ising Model ◽  
Low Temperature ◽  
Temperature Expansion

scholarly journals Low temperature expansion for the Ising model

1992 ◽  
Vol 69 (13) ◽  
pp. 1841-1844 ◽  
Author(s):  
Gyan Bhanot ◽  
Michael Creutz ◽  
Jan Lacki
Keyword(s):  
Ising Model ◽  
Low Temperature ◽  
Temperature Expansion

Calculation and computation

2021 ◽  
pp. 217-252
Author(s):  
James P. Sethna
Keyword(s):  
Monte Carlo ◽  
Perturbation Theory ◽  
Phase Transitions ◽  
Ising Model ◽  
Low Temperature ◽  
Markov Chains ◽  
Detailed Balance ◽  
Reaction Rates ◽  
Temperature Expansion ◽  
Monte Carlo Techniques

This chapter introduces Monte-Carlo techniques to simulate the equilibrium properties of complex systems, and perturbative techniques to calculate their behavior as an expansion about solvable limits. It uses the Ising model as a description of magnets, of binary alloys, and of the liquid-gas transition. It introduces Markov chains and detailed balance as providing a guarantee that Monte-Carlo methods converge to equilibrium. To analyze phases and phase transitions, it introduces a 27-term low-temperature expansion for the magnetization of the Ising model. Inside phases, perturbation theory converges; at phase transitions, it cannot. Exercises simulate the behavior of the Ising model and cellular function. They explore equilibration algorithms and calculation of low temperature expansions. And they apply Markov chains to coin flips, unicycles, fruit flies, chemical reaction rates, and DNA replication.

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