We present a simple method to estimate the central charge of the conformal field theory corresponding to a critical point of a two-dimensional lattice model from Monte Carlo simulations. The main idea is to use the Wang-Landau flat-histogram algorithm, which allows us to obtain the free energy of a lattice model on a torus as a function of torus radii. The central charge is calculated with good precision from a free-energy scaling at the critical point. We apply the method to the Ising, tricritical Ising (Blume-Capel), Potts, and site-diluted Ising models, and we also discuss an estimation of the conformal weights.We present a simple method to estimate the central charge of the conformal field theory corresponding to a critical point of a two-dimensional lattice model from Monte Carlo simulations. The main idea is to use the Wang-Landau flat-histogram algorithm, which allows us to obtain the free energy of a lattice model on a torus as a function of torus radii. The central charge is calculated with good precision from a free-energy scaling at the critical point. We apply the method to the Ising, tricritical Ising (Blume-Capel), Potts, and site-diluted Ising models, and we also discuss an estimation of the conformal weights.

arXiv:1612.06374Physical review. EJun 14, 20175 citations

Extending Monte Carlo samples

Bernard B. Beard

Nuclear Physics B - Proceedings SupplementsMay 1, 20031 citation

Monte Carlo method to calculate the central charge and critical exponents

Paul J. M. Bastiaansen, H. J. F. Knops

We present a finite size scaling technique to calculate the central charge and some critical exponents of two-dimensional critical models with a Monte Carlo simulation. We use systems with dimensions $L\ifmmode\times\else\texttimes\fi{}M,$ and focus on the scaling behavior in $M/L.$ The finite size scaling relation that we use is the universal expression for the stress tensor on the torus. The stress tensor is the operator that governs the anisotropy of the system, and stems for the theory of conformal invariance. We show that a lattice representation of the stress tensor can easily be constructed, such that its expectation value on the torus can be calculated in a Monte Carlo simulation. In doing so, we observe that the stress tensor turns out to be remarkably insensitive to critical slowing down. We show that the typical simulation time scales with the linear system dimension $L$ roughly as ${L}^{4},$ and that this scaling holds for the ordinary Metropolis algorithm as well as for more sophisticated cluster algorithms, such that it is fruitless to invoke the latter. We test the method for the Ising model (with central charge $c=$ $\frac{1}{2}$ ), the Ashkin-Teller model $(c=1),$ and the F model (also $c=1$ ).We present a finite size scaling technique to calculate the central charge and some critical exponents of two-dimensional critical models with a Monte Carlo simulation. We use systems with dimensions $L\ifmmode\times\else\texttimes\fi{}M,$ and focus on the scaling behavior in $M/L.$ The finite size scaling relation that we use is the universal expression for the stress tensor on the torus. The stress tensor is the operator that governs the anisotropy of the system, and stems for the theory of conformal invariance. We show that a lattice representation of the stress tensor can easily be constructed, such that its expectation value on the torus can be calculated in a Monte Carlo simulation. In doing so, we observe that the stress tensor turns out to be remarkably insensitive to critical slowing down. We show that the typical simulation time scales with the linear system dimension $L$ roughly as ${L}^{4},$ and that this scaling holds for the ordinary Metropolis algorithm as well as for more sophisticated cluster algorithms, such that it is fruitless to invoke the latter. We test the method for the Ising model (with central charge $c=$$\frac{1}{2}$), the Ashkin-Teller model $(c=1),$ and the F model (also $c=1$).

arXiv:cond-mat/9710098Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsApr 1, 199816 citations

Monte Carlo Studies of Many-Electron Systems

Robert L. Sugar

Springer proceedings in physicsJan 1, 19900 citations

Monte Carlo transfer-matrix study of the frustratedXYmodel

Joseph Marie Thijssen, H. J. F. Knops

We discuss the critical behavior of several models, all related to the 19-vertex model. These models combine Ising and Gaussian degrees of freedom and have central charge c=3/2 at the critical point. We present arguments why the frustrated XY model, which also has Gaussian and Ising degrees of freedom, might fall into a different universality class. We use the Monte Carlo transfer-matrix method of Bl\"ote and Nightingale to obtain accurate numerical results for the central charge and exponents of the frustrated XY model. In particular, we test the prediction for the central charge c to be equal to 3/2 also in this model. We find c=1.66\ifmmode\pm\else\textpm\fi{}0.04 for the central charge of the frustrated XY model at the critical point. It is not clear at this stage to which universality class this critical behavior belongs.We discuss the critical behavior of several models, all related to the 19-vertex model. These models combine Ising and Gaussian degrees of freedom and have central charge c=3/2 at the critical point. We present arguments why the frustrated XY model, which also has Gaussian and Ising degrees of freedom, might fall into a different universality class. We use the Monte Carlo transfer-matrix method of Bl\"ote and Nightingale to obtain accurate numerical results for the central charge and exponents of the frustrated XY model. In particular, we test the prediction for the central charge c to be equal to 3/2 also in this model. We find c=1.66\ifmmode\pm\else\textpm\fi{}0.04 for the central charge of the frustrated XY model at the critical point. It is not clear at this stage to which universality class this critical behavior belongs.

Physical review. B, Condensed matterAug 1, 199055 citations

M/L.

The finite size scaling relation that we use is the universal expression for the stress tensor on the torus. The stress tensor is the operator that governs the anisotropy of the system, and stems for the theory of conformal invariance. We show that a lattice representation of the stress tensor can easily be constructed, such that its expectation value on the torus can be calculated in a Monte Carlo simulation. In doing so, we observe that the stress tensor turns out to be remarkably insensitive to critical slowing down. We show that the typical simulation time scales with the linear system dimension

L

roughly as

{L}^{4},

and that this scaling holds for the ordinary Metropolis algorithm as well as for more sophisticated cluster algorithms, such that it is fruitless to invoke the latter. We test the method for the Ising model (with central charge

c=

\frac{1}{2}

), the Ashkin-Teller model

(c=1),

and the F model (also

c=1