Monte carlo calculations of the conformal charge

G. T. Barkema, John McCabe

J. Hove

We describe a method for calculating the density of states by combining several canonical Monte Carlo runs. We discuss how critical properties reveal themselves in g (epsilon) and demonstrate this by applying the method to several different phase transitions. We also demonstrate how this can used to calculate the conformal charge, where the dominating numerical method has traditionally been the transfer matrix.

P.G. Lauwers, Gunter Markus Schutz

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 $c=1$).

Svetlana Sokolova

Debasish Banerjee, Shailesh Chandrasekharan A, Domenico Orlando +1 more

We study the O(4) Wilson-Fisher fixed point in 2+1 dimensions in fixed large-charge sectors identified by products of two spin-j representations (j_{L},j_{R}). Using effective field theory we derive a formula for the conformal dimensions D(j_{L},j_{R}) of the leading operator in terms of two constants, c_{3/2} and c_{1/2}, when the sum j_{L}+j_{R} is much larger than the difference |j_{L}-j_{R}|. We compute D(j_{L},j_{R}) when j_{L}=j_{R} with Monte Carlo calculations in a discrete formulation of the O(4) lattice field theory, and show excellent agreement with the predicted formula and estimate c_{3/2}=1.068(4) and c_{1/2}=0.083(3).