Abstract
The simplest phase transition that remains a mystery may be the exit out of the ``deconfined'' phase in the self-dual Ising gauge model. Using simulations and theory, a new analysis explores what happens at that transition.
Highlights
Continuum field theory provides a language for a huge range of classical and quantum phase transitions [1,2], including many cases for which a simple Landau-Ginsburg formulation is insufficient [3,4,5,6,7,8,9,10]
We propose an explicit construction of the fictitious Ising field
We begin by reviewing several equivalent formulations of the partition function we study and the basic features of the phase diagram
Summary
Continuum field theory provides a language for a huge range of classical and quantum phase transitions [1,2], including many cases for which a simple Landau-Ginsburg formulation is insufficient [3,4,5,6,7,8,9,10]. We relate the feasibility of this patching operation to the question of whether e and m worldlines “percolate” in spacetime, and we obtain the phase diagram for this percolation [6] numerically This approach shows that the fictitious Ising fields can be constructed on the Ising* transition lines, but not at the self-dual critical point. The Z2 deconfined phase is adjacent to another family of critical “quantum loop models” [56,57,58,59,60] with no known Lagrangian description [60] While these critical points may again be viewed in terms of membranes in spacetime, the obstacle to a continuum description is different there: a topological constraint on the dynamics, rather than the existence of massless particles with nontrivial braiding. These different kinds of examples suggest that statistical ensembles of membranes [61] in three and four dimensions (elementary “string field theories” [62,63,64]) still hold many lessons for critical phenomena
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