Critical properties of the Antiferromagnetic \RP2$ model in three dimensions

Abstract

We study the behavior of the antiferromagnetic RP${}^2$ model in $d=3$. The vacuum structure is analyzed in the critical and low temperature regions, paying special attention to the spontaneous symmetry breaking pattern. Near the critical point we observe a full breakdown of the O(3) symmetry of the action. Several methods for computing critical exponents are compared. We conclude that the most solid determination is obtained using a measure of the correlation length. Corrections-to-scaling are parameterized, yielding a very accurate determination of the critical coupling and a 5\% error measure of the related exponent. This is used to estimate the systematic errors due to finite-size effects.

31 pages, 10 postscript figures

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• Finite size effects on measures of critical exponents in d=3 O(N) models
• New Universality Class in three dimensions: the Antiferromagnetic $R{P}^2$ model
• A Monte Carlo study of O(3) antiferromagnetic models in three dimensions
• Phase diagram of d=4 Ising Model with two couplings

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