Topic
Ice-type model
About: Ice-type model is a research topic. Over the lifetime, 5 publications have been published within this topic receiving 280 citations. The topic is also known as: six-vertex model.
Papers
TL;DR: Tem Temperley and Lieb (Proc. R. Soc., vol.A322, p.251 of 1971) have used operator methods to show that, for a square lattice, this problem is in turn equivalent to a staggered ice-type model as discussed by the authors.
Abstract: The partition function of the Potts model (1952) on any lattice can readily be written as a Whitney polynomial (1932). Temperley and Lieb (Proc. R. Soc., vol.A322, p.251 of 1971) have used operator methods to show that, for a square lattice, this problem is in turn equivalent to a staggered ice-type model. Here the authors rederive this equivalence by a graphical method, which they believe to be simpler, and which applies to any planar lattice. For instance, they also show that the Potts model on the triangular or honeycomb lattice is equivalent to an ice-type model on a Kagome lattice.
295 citations
TL;DR: In this paper, the authors present a theoretically estimated low-temperature entropy and compare it with numerical results, and consider the mapping between this model and the three-colour problem, i.e. colouring a regular graph with coordination equal to 4 (a two-dimensional lattice) with three colours, for which they apply the transfer-matrix method to calculate all allowed configurations for two dimensional square lattices of N oxygen atoms ranging from 4 to 225.
Abstract: The ice-type model proposed by Linus Pauling to explain its entropy at low temperatures is here approached in a didactic way. We first present a theoretically estimated low-temperature entropy and compare it with numerical results. Then, we consider the mapping between this model and the three-colour problem, i.e. colouring a regular graph with coordination equal to 4 (a two-dimensional lattice) with three colours, for which we apply the transfer-matrix method to calculate all allowed configurations for two-dimensional square lattices of N oxygen atoms ranging from 4 to 225. Finally, from a linear regression of the transfer matrix results, we obtain an estimate for the case N → ∞ which is compared with the exact solution by Lieb.
1 citations
TL;DR: In this paper, the authors present a theoretically estimated low-temperature entropy and compare it with numerical results, and consider the mapping between this model and the three-colour problem, i.e.,colouring a regular graph with coordination equal to 4 (a two-dimensional lattice) with three colours, for which they apply the transfer-matrix method to calculate all allowed configurations for 2D square lattices of oxygen atoms ranging from 4 to 225.
Abstract: The ice-type model proposed by Linus Pauling to explain its entropy at low temperatures is here approached in a didactic way. We first present a theoretically estimated low-temperature entropy and compare it with numerical results. Then, we consider the mapping between this model and the three-colour problem, i.e.,colouring a regular graph with coordination equal to 4 (a two-dimensional lattice) with three colours, for which we apply the transfer-matrix method to calculate all allowed configurations for two-dimensional square lattices of $N$ oxygen atoms ranging from 4 to 225. Finally, from a linear regression of the transfer matrix results, we obtain an estimate for the case $N\rightarrow \infty $ which is compared with the exact solution by Lieb.
TL;DR: In this paper, a new model called the Temperley-Lieb interactions model was introduced, in two-dimensional lattice statistics, on a square lattice ℒ, and a graphical equivalence of this model to the six-vertex, self-dual Potts, critical hard-hexagons and critical nonintersecting string models was established.
Abstract: A new model (called the Temperley-Lieb interactions model) is introduced, in two-dimensional lattice statistics, on a square lattice ℒ. The Temperley-Lieb equivalence of this model to the six-vertex, self-dual Potts, critical hard-hexagons and critical nonintersecting string models is established. A graphical equivalence of this model to the six-vertex model generalizes this equivalence to noncritical cases of the above models. The order parameters of a specialization of this model are studied.
TL;DR: The scaling limit of the Hubbard model, the massive Thirring model and the broken SU(2) massive fermion model of Bukhvostov and Lipatov were shown to be the scaling limit in this paper.
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2020 | 1 |
| 1987 | 1 |
| 1984 | 1 |
| 1976 | 1 |