A Monte Carlo study of Inverse Symmetry Breaking

Is it always true that more heat means more disorder? The intuitive answer to this question would be yes and indeed this is what happens in the majority of physical systems. Nevertheless, over 20 years ago, S. Weinberg [1], quoting an unpublished remark by S. Coleman, observed that there may be exceptions to the general rule: in models with a sufficiently rich scalar sector, some of the scalars may acquire a negative Debye mass, with the result that the symmetric vacuum becomes necessarily unstable at high temperatures. This remarkable phenomenon is called Inverse-Symmetry-Breaking (ISB) or Symmetry-Non-Restoration (SNR) depending on the symmetry of the ground state at zero temperature. The possibility of ISB and SNR in realistic particle models and their cosmological consequences have been explored in a number of papers [2]. Weinberg’s analysis of ISB and SNR was based on a simple one-loop approximation and some authors have questioned its reliability. Subsequent studies, using different approximations with various amounts of non-perturbative content, produced contradictory results. While some concluded that ISB and SNR cannot occur [3], others found that they do occur [4], even though (in the majority of the cases) in a region of the parameter space significantly reduced with respect to the one-loop result . In this paper we present the first Monte Carlo study of ISB in 4 dimensions in a two-scalar model, with a global Z2×Z2 symmetry. The job was mainly carried out on our RTNN computer, which holds 32 PentiumPro processors, for a total CPU time of approximately two months of the whole machine. The results were analogous to those found in 2+1 dimensions [5] and seem to show that ISB is absent for certain values of the renormalized couplings in the region for which perturbation theory predicts it, in accordance with the theorem proven in [6]. The model we simulated is described by the bare (euclidean) action: