Finite-Size Scaling in Strips: Antiperiodic Boundary Conditions

Theodore W. Burkhardt, Ihnsouk Guim

The authors give exact results for the energy spectrum of a chain of N Ising spins in a transverse field with periodic, free, and antiperiodic boundary conditions. The dependence of the energy gaps on boundary conditions is compatible with predictions of conformal invariance for correlation lengths in two-dimensional strips. The feasibility of calculating surface critical indices using phenomenological renormalisation with free boundary conditions and the convergence for large N are discussed.

John Cardy

John Cardy

Ming-Chang Huang, Tsong‐Ming Liaw, Yu-Pin Luo +1 more

The critical properties of an infinitely long Ising strip with finite width L joined periodically or antiperiodically are investigated by analyzing the distribution of partition function zeros. For periodic boundary condition, the the leading finite-size scaling of partition function zeros and its corrections are given. For antiperiodic boundary condition, the critical point of 2D Ising transition is one of the loci of the zeros, and the associated non-analyticity is identified as a first-order phase transition. The exact amount of the latent heat released by the transition is 4/L.

Martin Weigel, Wolfhard Janke E

In a Monte Carlo study using a cluster update algorithm we investigate finite-size scaling (FSS) of the correlation lengths of several representatives of the class of three-dimensional classical $\mathrm{O}(n)$ symmetric spin models on the geometry ${T}^{2}\ifmmode\times\else\texttimes\fi{}R$. For all the models we find strong evidence of a linear relation between FSS amplitudes and scaling dimensions when applying antiperiodic instead of periodic boundary conditions across the torus. This type of scaling relation can be proven analytically for systems on two-dimensional strips with periodic boundary conditions using conformal field theory.

Vladimir Privman A