A Proof that the Free Energy of a Spin System is Extensive

1964 ◽  
Vol 5 (9) ◽  
pp. 1215-1222 ◽  
Author(s):  
Robert B. Griffiths
Keyword(s):  
Free Energy ◽  
Spin System

scholarly journals Approximation of the n-vicinity method

2019 ◽  
Vol 487 (3) ◽  
pp. 246-251
Author(s):  
B. V. Kryzhanovsky
Keyword(s):  
Free Energy ◽  
Small Parameter ◽  
Spin System ◽  
Nearest Neighbors ◽  
Spin Systems

We determined a small parameter that determines the possibility of using the n-vicinity 06_method to calculate the free energy of a spin system, and found the types of spin systems for which this method is applicable. It is shown that this method is applicable for the analysis of spin systems, where the number of nearest neighbors is greater than 16/3.

scholarly journals Exact Solution of a One-dimensional Spin System

1970 ◽  
Vol 23 (5) ◽  
pp. 927 ◽  
Author(s):  
RW Gibberd
Keyword(s):  
Phase Transition ◽  
Exact Solution ◽  
Free Energy ◽  
Partition Function ◽  
Thermodynamic Limit ◽  
Spin System ◽  
Spin Systems ◽  
One Dimensional ◽  
Gibb’S Free Energy ◽  
Theory Of Superconductivity

The partition function and the Gibb's free energy are calculated exactly in the thermodynamic limit, using techniques which are well known in the theory of superconductivity. This calculation illustrates explicitly the similarity between the phase transition in superconductivity and the molecular field transitions in spin systems.

ON THE DETERMINATION OF CRITICAL POINT IN HIGHER-ORDER VARIATIONAL CUMULANT EXPANSION

1996 ◽  
Vol 10 (12) ◽  
pp. 531-536 ◽  
Author(s):  
X.F. OU ◽  
J.T. OU ◽  
D.L. LIN
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Phase Transitions ◽  
Ising Model ◽  
Critical Point ◽  
Spin System ◽  
Order Approximation ◽  
Two Dimensional ◽  
Cumulant Expansion

To the lowest order approximation, the method of variational cumulant expansion has been successful in the determination of the critical point of a spin system on the Ising model. In the second order calculation, unphysical phase transition arises. In this letter, we first analyze the origin of unphysical phase transitions in high-order variational cumulant expansion calculations. We then explain the basis on which a conjecture is proposed that to any order m of the variational cumulant expansion, the critical point is given by the bifurcation point of the free energy. The theory is finally verified numerically for the two-dimensional case.

Free energy and Green function for the multi-coupled spin system

2001 ◽  
Vol 34 (43) ◽  
pp. 9109-9122
Author(s):  
Zhi-Ming Bai ◽  
Ya-Ru Wang ◽  
Zhan Xu ◽  
Mo-Lin Ge
Keyword(s):  
Free Energy ◽  
Green Function ◽  
Spin System

Encultured minds, not error reduction minds

2020 ◽  
Vol 43 ◽  
Author(s):  
Robert Mirski ◽  
Mark H. Bickhard ◽  
David Eck ◽  
Arkadiusz Gut
Keyword(s):  
Free Energy ◽  
Error Reduction ◽  
Energy Principle ◽  
Free Energy Principle ◽  
Current Article

Abstract There are serious theoretical problems with the free-energy principle model, which are shown in the current article. We discuss the proposed model's inability to account for culturally emergent normativities, and point out the foundational issues that we claim this inability stems from.

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