Critical points of Potts and O(N) models from eigenvalue identities in periodic Temperley–Lieb algebras

@article{Jacobsen2015CriticalPO,
  title={Critical points of Potts and O(N) models from eigenvalue identities in periodic Temperley–Lieb algebras},
  author={Jesper Lykke Jacobsen},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2015},
  volume={48}
}
  • J. Jacobsen
  • Published 10 July 2015
  • Mathematics
  • Journal of Physics A: Mathematical and Theoretical
In previous work with Scullard, we have defined a graph polynomial PB(q, T) that gives access to the critical temperature Tc of the q-state Potts model defined on a general two-dimensional lattice  . ?> It depends on a basis B, containing n × m unit cells of  , ?> and the relevant root Tc(n, m) of PB(q, T) was observed to converge quickly to Tc in the limit n , m → ∞ . ?> Moreover, in exactly solvable cases there is no finite-size dependence at all. In this paper we show how to reformulate… 

Potts-model critical manifolds revisited

We compute critical polynomials for the q-state Potts model on the Archimedean lattices, using a parallel implementation of the algorithm of Jacobsen (2014 J. Phys. A: Math. Theor 47 135001) that

Q-colourings of the triangular lattice: exact exponents and conformal field theory

We revisit the problem of Q-colourings of the triangular lattice using a mapping onto an integrable spin-one model, which can be solved exactly using Bethe ansatz techniques. In particular we focus

Spaces of states of the two-dimensional O(n) and Potts models

We determine the spaces of states of the two-dimensional O(n) and Q-state Potts models with generic parameters n,Q ∈ C as representations of their known symmetry algebras. While the relevant

Bootstrap approach to geometrical four-point functions in the two-dimensional critical Q-state Potts model: a study of the s-channel spectra

A bstractWe revisit in this paper the problem of connectivity correlations in the Fortuin-Kasteleyn cluster representation of the two-dimensional Q-state Potts model conformal field theory. In a

Phase diagram of the triangular-lattice Potts antiferromagnet

We study the phase diagram of the triangular-lattice Q-state Potts model in the real (Q,v)-plane, where v=eJ−1 is the temperature variable. Our first goal is to provide an obviously missing feature

Bond percolation thresholds on Archimedean lattices from critical polynomial roots

We present percolation thresholds calculated numerically with the eigenvalue formulation of the method of critical polynomials; developed in the last few years, it has already proven to be orders of

On the growth constant for square-lattice self-avoiding walks

The growth constant for two-dimensional self-avoiding walks on the honeycomb lattice was conjectured by Nienhuis in 1982, and since that time the corresponding results for the square and triangular

The three-state Potts antiferromagnet on plane quadrangulations

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.

Correlation function behavior in the topological Kosterlitz–Thouless transition using the Replica-Exchange Wang–Landau technique

In this paper, we use the Replica-Exchange Wang–Landau (REWL) technique to study the behavior of the two-point correlation function of the site diluted classical anisotropic Heisenberg (AH) model in

Critical p=1/2 in percolation on semi-infinite strips.

  • Z. Koza
  • Mathematics
    Physical review. E
  • 2019
It is argued that the probability that a cluster touches the three sides of a planar system at the percolation threshold has a continuous limit of 1/2 and that this limit is universal for planar systems.

References

SHOWING 1-10 OF 51 REFERENCES

High-precision percolation thresholds and Potts-model critical manifolds from graph polynomials

The critical curves of the q-state Potts model can be determined exactly for regular two-dimensional lattices G that are of the three-terminal type. This comprises the square, triangular, hexagonal

Critical manifold of the kagome-lattice Potts model

Any two-dimensional infinite regular lattice G can be produced by tiling the plane with a finite subgraph B⊆G; we call B a basis of G. We introduce a two-parameter graph polynomial PB(q, v) that

Transfer matrix computation of critical polynomials for two-dimensional Potts models

In our previous work [1] we have shown that critical manifolds of the q-state Potts model can be studied by means of a graph polynomial PB(q, v), henceforth referred to as the critical polynomial.

The dilute Temperley–Lieb O(n  =  1) loop model on a semi infinite strip: the ground state

It is shown that all ground state components can be recovered for arbitrary L using the qKZ equation and certain recurrence relation.

The periodic sℓ(2|1) alternating spin chain and its continuum limit as a bulk logarithmic conformal field theory at c = 0

A bstractThe periodic sℓ(2|1) alternating spin chain encodes (some of) the properties of hulls of percolation clusters, and is described in the continuum limit by a logarithmic conformal field theory

Critical behaviour and conformal anomaly of the O(n) model on the square lattice

Finite-size scaling and transfer-matrix techniques are used to determine the conformal anomaly and critical exponents of O(n) models on the square lattice. These calculations were performed on five
...