On the phase transition of the Ising gauge model

Valeriy A Ryabov

N.S. Ananikian, Ruben G. Ghulghazaryan, N. Sh. Izmailian +1 more

The exact solution of a general Z(4) gauge Potts model with a single and double plaquette representation of the action is found on a subspace of gauge-coupling parameters on the square and triangular lattices. The two Ising-type critical lines of a second-order phase transition for the model on a square lattice are found. For the model on a triangular lattice the two critical surfaces of an Ising-type and two nontrivial lines of a second-order phase transition with different critical behavior than on the critical surfaces are found. It is shown that a two-dimensional (2D) general Z(4) gauge Potts model with single and double plaquette representation of the action and a 2D spin-3 / 2 Ising model belong to the same universality class.

Tomoyuki Morishita, Synge Todo

Recently, machine learning has been applied successfully for identifying phases and phase transitions of the Ising models. The continuous phase transition is characterized by spontaneous symmetry breaking, which can not be detected in general from a single spin configuration. To investigate if neural networks can extract correlations among spin snapshots, we propose a new test using the random-gauge Ising model. We show that neural networks can extract the order parameter or the energy of the random-gauge model as in the ferromagnetic case. We also discuss how and where the information of random gauge is encoded in neural networks and attempt to reconstruct the gauge from the neural network parameters. We find that the fully connected network encodes the effect of random gauge to its weights naturally. In contrast, the convolutional network copes with the randomness by assigning different network parts to local gauge patterns. This observation indicates that although the latter demonstrates higher performance than the former for the present randomized-gauge test, the former is more effective and suitable for dealing with models with spatial randomness.

H Ulman, M Athematics J Ournal

Tomoyasu Tanaka

Loïc Turban

The two-dimensional version of a generalised Ising gauge theory in which the gauge part of the action involves a product of Ising link variables around every rectangular 2*1 face of the lattice is studied. The pure gauge theory is related to the Ising model and is self-dual. The gauge plus matter theory is also self-dual. For negative gauge coupling an Ising critical line in the ( beta g , beta m ) plane separates a phase with staggered frustration from another which is homogeneously frustrated.