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Order parameter conditions from mutual information and symmetry conditions

Ivan Arraut, Wing Chi Yu

Abstract

The mutual information method has demonstrated to be very useful for deriving the potential order parameter of a system. Although the method suggests some constraints which help to define this quantity, there is still some freedom in the definition. The method then results inefficient for cases where we have order parameters with a large number of constants in the expansion, which happens when we have many degenerate vacuums. Here we introduce some additional constraints based on the existence of broken symmetries, which help us to reduce the arbitrariness in the definitions of the order parameter in the proposed mutual information method.

Order parameter conditions from mutual information and symmetry conditions

Abstract

The mutual information method has demonstrated to be very useful for deriving the potential order parameter of a system. Although the method suggests some constraints which help to define this quantity, there is still some freedom in the definition. The method then results inefficient for cases where we have order parameters with a large number of constants in the expansion, which happens when we have many degenerate vacuums. Here we introduce some additional constraints based on the existence of broken symmetries, which help us to reduce the arbitrariness in the definitions of the order parameter in the proposed mutual information method.

Paper Structure

This paper contains 11 sections, 45 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Vacuum degeneracy and spontaneous symmetry breaking
  3. Example: Ferromagnetism
  4. The mutual information method and the construction of a local order operator
  5. The local order operator
  6. Additional conditions: General broken symmetries of the system
  7. Mapping one vacuum into another one with the same energy level via broken symmetry
  8. Applications
  9. Ferromagnetic long-range order
  10. One dimensional ferromagnetic
  11. Conclusions

Figures (1)

  • Figure 1: Typical potential of the $\sigma$-model. For certain combination of parameters, the potential develops a multiplicity of ground states (vacuums).