Boundary-field-driven control of discontinuous phase transitions on hyperbolic lattices

TL;DR

This study investigates how boundary magnetic fields influence discontinuous phase transitions in Potts models on hyperbolic lattices, revealing that such transitions can be continuously controlled via boundary effects, unlike on Euclidean lattices.

Contribution

The paper introduces a boundary-field-driven approach to control discontinuous phase transitions on hyperbolic lattices, highlighting the role of boundary effects and the bulk excess free energy.

Findings

Boundary magnetic fields significantly affect first-order phase transitions.

Discontinuous transitions on hyperbolic lattices can be continuously tuned by boundary fields.

False phase transitions diminish as more boundary layers are contracted.

Abstract

The multistate Potts models on two-dimensional hyperbolic lattices are studied with respect to various boundary effects. The free energy is numerically calculated by Corner Transfer Matrix Renormalization Group method. We analyze phase transitions of the Potts models in the thermodynamic limit with respect to contracted boundary layers. A false phase transition is present even if a couple of the boundary layers are contracted. Its significance weakens, as the number of the contracted boundary layers increases, until the correct phase transition (deep inside the bulk) prevails over the false one. For this purpose we derive a thermodynamic quantity, the so-called bulk excess free energy, which depends on the contracted boundary layers and memorizes additional boundary effects. In particular, the magnetic field is imposed on the outermost boundary layer. While the boundary magnetic field does not affect the second-order phase transition in the bulk if suppressing all the boundary effects on the hyperbolic lattices, the first-order (discontinuous) phase transition is significantly sensitive to the boundary magnetic field. Contrary to the phase transition on the Euclidean lattices, the discontinuous phase transition on the hyperbolic lattices can be continuously controlled (within a certain temperature coexistence region) by varying the boundary magnetic field.