Abstract
A family of one-dimensional classical chiral spin models with groupG=U(N) orSU(N) is introduced, having complex nearest-neighbor interaction. TheseG×G invariant systems have self-adjoint positive transfer matrices and satisfy reflection positivity. In the case ofG=U(N), forN=1, 2, 3, sequences of first-order phase transitions are shown to occur.
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References
T. D. Lee and C. N. Yang, Statistical theory of equations of state and phase transitions I, II,Phys. Rev. 87:404, 410 (1952).
G. Gallavotti and J. L. Lebowitz, Some remarks on Ising-spin systems,Physica 70:219 (1973).
M. Asorey and J. G. Esteve, First-order transitions in one-dimensional systems with local couplings,J.Stat. Phys. 65:483 (1991).
E. Hewitt and K. A. Ross,Abstract Harmonic Analysis, Vol. II, Section 27. Springer-Verlag, Berlin.
K. Osterwalder and E. Seiler, Gauge field theories on a lattice,Ann. Phys. (N.Y.)110:440 (1978).
H. Weyl,The Classical Groups (Princeton University Press, Princeton, New Jersey).
G. N. Watson,A Treatise on the Theory of Bessel Functions (Cambridge University Press, Cambridge).
R. B. Israel,Convexity in the Theory of Lattice Gases (Princeton University Press, Princeton, New Jersey).
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Müller, V.F. One-dimensional chiral models with first-order phase transitions. J Stat Phys 70, 1349–1363 (1993). https://doi.org/10.1007/BF01049437
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DOI: https://doi.org/10.1007/BF01049437