• Corpus ID: 118142293

Entropic Coulomb Forces in Ising and Potts Antiferromagnets and Ice Models

  title={Entropic Coulomb Forces in Ising and Potts Antiferromagnets and Ice Models},
  author={Cristopher Moore and Mats G. Nordahl and Nelson Minar and Cosma Rohilla Shalizi},
We study topological defects in the triangular Ising antiferromagnet, a related model on the square lattice equivalent to the six-vertex ice model, and the three-state antiferromagnetic Potts model on the square lattice. We suggest that in each case, defects are attracted or repelled with a Coulomb force mediated through correlations in the surrounding lattice. Since the energy of the two defects does not depend on the distance between them, this force is entropically driven. We give numerical… 

Height Representation, Critical Exponents, and Ergodicity in the Four-State Triangular Potts Antiferromagnet

We study the four-state antiferromagnetic Potts model on the triangular lattice. We show that the model has six types of defects which diffuse and annihilate according to certain conservation laws

Role of topological defects in breaking and enhancing discrete symmetries[HBNI Th111]

Phase transitions accompanied by spontaneous breaking of continuous symmetries have been studied extensively in condensed matter and high energy physics. In this thesis we investigate the spontaneous

An information-theoretic formulation of Newton's second law

From the principle of maximum entropy for a closed system in thermal equilibrium, for the first instance a clear relation is shown to exist between total entropy S (in terms of arrangements of



A constrained Potts antiferromagnet model with an interface representation

We define a 4-state Potts model ensemble on the square lattice, with the constraints that neighbouring spins must have different values, and that no plaquette may contain all four states. The spin

Long-range order for antiferromagnetic Potts models.

  • Koteck
  • Physics
    Physical review. B, Condensed matter
  • 1985
Long-range order for the three-state antiferromagnetic Potts model may appear at zero temperature as an instability with respect to boundary conditions. It is studied using an approximate

Critical antiferromagnetic square-lattice Potts model

  • R. Baxter
  • Physics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1982
The critical temperature of the antiferromagnetic q-state Potts model on the square lattice is located, and the critical free energy and internal energy are evaluated. As with the ferromagnetic

Roughening transitions and the zero-temperature triangular Ising antiferromagnet

The zero-temperature triangular Ising antiferromagnet is mapped onto a solid-on-solid (SOS) model. The system undergoes a roughening transition characterised by a critical exponent alpha =1/2, by the

Antiferromagnetic Potts Models on the Square Lattice: A High-Precision Monte Carlo Study

We study the antiferromagnetic q-state Potts model on the square lattice for q=3 and q=4, using the Wang–Swendsen–Kotecký (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation

Antiferromagnetic Potts models.

The low-temperature phase in three dimensions is shown to have long-range order with a finite-size dependence similar to that of the XY model.

Possibility of the Kosterlitz-Thouless Phase Transition in the Two Dimensional Fully Frustrated Ising Model

Fully frustrated Ising models on two-dimensional lattice with the first and second or third nearest neighbor interactions are studied. Original Ising spin variables are transformed into the cell spin

Occurrence of Kosterlitz-Thouless-Like Phase Transition in Antiferromagnetic Potts Models

Monte Carlo simulations of three-state Potts models interacting with nearest-neighbor antiferromagnetic J 1 ( 0) are carried out on a square lattice. At enough low temperatures an antiferromagnetic

Monte Carlo study of the three-state square Potts antiferromagnet

The role of a new type of vortices introduced in the three-state squares Potts antiferromagnet for decay of correlations is considered. Fluctuations of the vortex charge in a region are measured

The anhydrous alums as model triangular-lattice magnets

We show that materials based on the yavapaiite layered structure are of potential interest as realizations of a model quasi-two-dimensional triangular-lattice antiferromagnet. The structure type is