Abstract
We consider an Ising system in d≥2 dimensions with a ferromagnetic Kac potential whose scaling parameter is denoted by γ. We derive an asymptotic series for the thermodynamic pressure P β, γ in powers of γ. The 0th-order term of the expansion is the mean-field pressure of the Lebowitz and Penrose theory.
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REFERENCES
O. Benois, T. Bodineau, P. Buttà, and E. Presutti, On the validity of van der Waals theory of surface tension, Markov Processes and Related Fields 3:175–198 (1997).
O. Benois, T. Bodineau, and E. Presutti, Large deviations in the van der Waals limit, Stochastic Proc. and their Appl. 75:89–104 (1998).
P. Buttà, I. Merola, and E. Presutti, On the validity of the van der Waals theory, Markov Processes and Related Fields 3:63–88 (1997).
M. Cassandro, R. Marra, and E. Presutti, Upper bounds on the critical temperature for Kac potential, J. Stat. Phys. 88(3–4):537–566 (1997). 1995.
M. Cassandro and E. Presutti, Phase transitions in Ising systems with long but finite range, Markov Processes and Related Fields 2:241–262 (1996).
R. L. Dobrushin, Prescribing a system of random variables by conditional distributions, Theory of Probability and Its Applications 3:458–486 (1970).
M. Kac, G. Uhlenbeck, and P. C. Hemmer, On the Van der Waals theory of vapour-liquid equilibrium. I. Discussion of a one dimensional model, J. Math. Phys. 4:216–228 (1963); II. Discussion of the distribution functions, J. Math. Phys. 4:229–247 (1963); III. Discussion of the critical region, J. Math. Phys. 5:60–74 (1964).
J. Lebowitz, G. Stell, S. Baer, and W. Theumann, Separation of the interaction potential into two parts in Statistical Mechanics, Part I, J. Math. Phys. 6:1282 (1965); Part II, J. Math. Phys. 7:1532 (1966).
J. Lebowitz, A. E. Mazel, and E. Presutti, Liquid-vapour phase transitions for systems with finite range interactions, submitted to J. Stat. Phys.
J. Lebowitz and O. Penrose, Rigorous treatment of the Van der Waals Maxwell theory of the liquid vapour transition, J. Math. Phys. 7:98–113 (1966).
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Merola, I. Asymptotic Expansion of the Pressure in the Inverse Interaction Range. Journal of Statistical Physics 95, 745–758 (1999). https://doi.org/10.1023/A:1004503611860
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DOI: https://doi.org/10.1023/A:1004503611860