Abstract
On an example of a simple spin system with two ground states and no symmetry, we show how to control low-temperature systems near first-order phase transitions by a straightforward renormalization group argument. The method, as opposed to the Pirogov-Sinai approach, also works for complex Hamiltonians.
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References
P. Bleher and Ya. Sinai, Investigation of the critical point in models of the type of Dyson's hierarchical models,Commun. Math. Phys. 33:23–42 (1973).
M. E. Fisher and A. Nihat Berker, Scaling for first-order phase transitions in ther-modynamic and finite systems,Phys. Rev. B 26:2507–2513 (1982).
R. B. Griffiths and P. A. Pearce, Position-space renormalization-group transformations: Some proofs and some problems,Phys. Rev. Lett. 41:917–923 (1978); Mathematical properties of position-space renormalization group transformations,J. Stat. Phys. 20:499–545 (1979).
R. Kotecký and D. Preiss, An inductive approach to Pirogov—Sinai theory,Rend. Circ. Matem. Palermo II(3) 1984:161–164.
R. Kotecký and D. Preiss, Cluster expansion for abstract polymer models,Commun. Math. Phys. 103:491–498 (1986).
C. M. Newman, Normal fluctuations and the FKG inequalities,Commun. Math. Phys. 74:119–128 (1980).
B. Nienhuis and M. Nauenberg, First order phase transitions in renormalization group theory,Phys. Rev. Lett. 35:477–479 (1975).
S. Pirogov, Coexistence of phases in multicomponent lattice liquid with complex thermodynamic parameters,Teor. Mat. Fiz. 66:331–335 (1986).
S. Pirogov and Ya. G. Sinai, Phase diagrams of classical lattice systems I and II,Teor. Mat. Fiz. 25:1185–1192 (1975); 26:39–49 (1976).
E. Seller,Gauge Theories As a Problem of Constructive Quantum Field Theory and Statistical Mechanics (Lecture Notes in Physics, Vol. 159, Springer, Berlin, 1982).
Ya. G. Sinai,Theory of Phase Transitions: Rigorous Results (Pergamon Press, Oxford, 1982).
K. G. Wilson and J. Kogut, The renormalization group and the e-expansion,Phys. Rep. 12C:75–200 (1974).
M. Zahradnik, An alternative version of Pirogov-Sinai theory,Commun. Math. Phys. 93:559–581 (1984); Stable and unstable phases in Pirogov-Sinai theory, p. 347–353 inProceedings of the VIIIth International Congress in Mathematical Physics, Marseille 1986, M. Mebkhout and R. Sénéor, eds. (World Scientific, Singapore, 1987).
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Gawedzki, K., Kotecký, R. & Kupiainen, A. Coarse-graining approach to first-order phase transitions. J Stat Phys 47, 701–724 (1987). https://doi.org/10.1007/BF01206154
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DOI: https://doi.org/10.1007/BF01206154