Journal of Statistical Physics

, Volume 34, Issue 5, pp 731–761

Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas

  • Bernard Nienhuis

DOI: 10.1007/BF01009437

Cite this article as:
Nienhuis, B. J Stat Phys (1984) 34: 731. doi:10.1007/BF01009437


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 theXY model and the clock models, the equivalence has been instrumental for almost our entire understanding of the critical behavior. Recently it was shown that theq-state Potts model and then-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 Coulombgas representation allows analytic calculation of some critical indices.

Key words

Two-dimensional spin models:XY, Z(p) Potts AshkinTellerO(n) SOS percolation SAW, andF model critical behavior critical indices Coulomb gas spin-wave and vortex operators Gaussian model 

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • Bernard Nienhuis
    • 1
  1. 1.Philips Natuurkundig LaboratoriumJA EindhovenNetherlands