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Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas. (English) Zbl 0595.76071
Summary: Many two-dimensional spin models can be transformed into Coulomb-gas systems in which charges interact via logarithmic potentials. For some models, such as the eight-vertex model and the Ashkin-Teller model, the Coulomb-gas representation has added significantly to the insight in the phase transitions. For other models, notably the XY model and the clock models, the equivalence has been instrumental for almost our entire understanding of the critical behavior.
Recently it was shown that the q-state Potts model and the n-vector model are equivalent to a Coulomb gas with an asymmetry between positive and negative charges. Fieldlike operators in these spin models transform noninteger charges and magnetic monopoles. With the aid of exactly solved models the Coulomb-gas representation allows analytic calculation of some critical indices.

MSC:
76N15 Gas dynamics (general theory)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B40 Kinetic theory of gases in equilibrium statistical mechanics
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