# Finite-temperature phase transition in a class of four-state Potts antiferromagnets.

@article{Deng2011FinitetemperaturePT, title={Finite-temperature phase transition in a class of four-state Potts antiferromagnets.}, author={Youjin Deng and Yu’an Huang and Jesper Lykke Jacobsen and Jes{\'u}s Salas and Alan D. Sokal}, journal={Physical review letters}, year={2011}, volume={107 15}, pages={ 150601 } }

We argue that the four-state Potts antiferromagnet has a finite-temperature phase transition on any Eulerian plane triangulation in which one sublattice consists of vertices of degree 4. We furthermore predict the universality class of this transition. We then present transfer-matrix and Monte Carlo data confirming these predictions for the cases of the Union Jack and bisected hexagonal lattices.

## 18 Citations

### Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models

- MathematicsCommunications in Mathematical Physics
- 2014

We prove the existence of long-range order at sufficiently low temperatures, including zero temperature, for the three-state Potts antiferromagnet on a class of quasi-transitive plane…

### Phase transitions in XY antiferromagnets on plane triangulations

- Physics
- 2013

Using Monte Carlo simulations and finite-size scaling, we investigate the XY antiferromagnet on the triangular, Union Jack and bisected-hexagonal lattices, and in each case find both Ising and…

### Three-state Potts model on the centered triangular lattice.

- PhysicsPhysical review. E
- 2020

This work studies phase transitions of the Potts model on the centered-triangular lattice with two types of couplings, namely, K between neighboring triangular sites, and J between the centered and the triangular sites and finds that there are, for all finite J, two transitions when K is varied.

### On the phase diagram of the random bond q-state Potts model

- MathematicsThe European Physical Journal B
- 2019

Abstract
We consider the two-dimensional random bond q-state Potts model within the recently introduced exact framework of scale invariant scattering, exhibit the line of stable fixed points induced…

### The three-state Potts antiferromagnet on plane quadrangulations

- PhysicsPhysical review. E
- 2018

A criterion based on graph duality to predict whether the three-state Potts antiferromagnet on a plane quadrangulation has a zero- or finite-temperature critical point, and its universality class, and it is found that the Wang-Swendsen-Kotecký algorithm has no critical slowing-down in the former case, and critical slowing down in the latter.

### Partial long-range order in antiferromagnetic Potts models

- Physics
- 2014

The Potts model plays an essential role in classical statistical mechanics, illustrating many fundamental phenomena. One example is the existence of partially long-range-ordered states, in which some…

### Accepted for publication in Communications in Mathematical Physics

- Mathematics
- 2014

We prove the existence of long-range order at sufficiently low temperatures, including zero temperature, for the three-state Potts antiferromagnet on a class of quasi-transitive plane…

### Partial Order in Potts Models on the Generalized Decorated Square Lattice

- Physics
- 2013

We explore the Potts model on the generalized decorated square lattice, with both nearest (J1) and next-nearest (J2) neighbor interactions. Using the tensor renormalization-group method augmented by…

### On superuniversality in the q-state Potts model with quenched disorder

- Physics
- 2017

We obtain the exact scale invariant scattering solutions for two-dimensional field theories with replicated permutational symmetry Sq. After sending to zero the number of replicas they correspond to…

### Discontinuous Spontaneous-Symmetry-Breaking in the Microcanonical Ensemble

- Physics
- 2019

Spontaneous-symmetry-breaking (SSB) is a macroscopic collective phenomenon occurring at phase transitions. Although deep understanding of SSB in the canonical statistical ensemble has been achieved,…

## References

SHOWING 1-10 OF 26 REFERENCES

### Phase transition in the three-state Potts antiferromagnet on the diced lattice.

- PhysicsPhysical review letters
- 2008

It is proved that the 3-state Potts antiferromagnet on the diced lattice (dual of the kagome lattice) has entropically driven long-range order at low temperatures (including zero) and Monte Carlo simulations of the3-state and 4-state models are presented.

### Partial order and finite-temperature phase transitions in Potts models on irregular lattices.

- PhysicsPhysical review letters
- 2011

Strong evidence is presented for a previously unknown, "entropy-driven," finite-temperature phase transition to a partially ordered state in the Potts model on the Union-Jack lattice.

### Exactly solved models in statistical mechanics

- Physics
- 1982

exactly solved models in statistical mechanics exactly solved models in statistical mechanics rodney j baxter exactly solved models in statistical mechanics exactly solved models in statistical…

### Phys

- 99, 629
- 2000

### and D

- Sénéchal, Conformal Field Theory
- 1997

### A 15

- 1982

### Proc

- Cambridge Philos. Soc. 48, 106
- 1952

### Here we exploit the algorithm of

- J. Phys. A
- 2010

### in Polygons

- Polyominoes and Polycubes, edited by A.J. Guttmann, Lecture Notes in Physics #775
- 2009

### the triangular-lattice antiferromagnetic spin-s Ising model for large enough s

- Phys. Rev. B
- 1997