Analytic calculations, Monte Carlo (MC) simulations [N. Metropolis and S. Ulam, J. Am. Stat.
Asso 44, 335 (1949)] and renormalization group (RG) theory [KG Wilson, Phys. Rev. B 4 …

We express the partition functions of the dimer model on finite square lattices under five
different boundary conditions (free, cylindrical, toroidal, Möbius strip, and Klein bottle) …

The shape-dependent universality of the excess percolation cluster number and cross-
configuration probability on a torus is examined. Besides the aspect ratio of the torus, the …

Let f N and ξ N− 1 represent, respectively, the free energy per spin and the inverse spin-spin
correlation length of the critical Ising model on a N×∞ lattice, with f N→ f∞ as N→∞. We …

We study the finite-size scaling properties of the Ising model on the Möbius strip and the
Klein bottle. The results are compared with those of the Ising model under different boundary …

Let f, U, and C represent, respectively, the free energy, the internal energy, and the specific
heat of the critical Ising model on the M× N square lattice with periodic boundary conditions …

We analyze the partition function of the dimer model on M× N triangular lattice wrapped on
the torus obtained by Fendley, Moessner, and Sondhi [Phys. Rev. B 66, 214513,(2002)] …

Using exact partition functions and finite-size corrections for the Ising model on finite square,
plane triangular, and honeycomb lattices and extending a method [J. Phys. 19, L1215 …

Based on the connection between the Ising model and a correlated percolation model, we
calculate the distribution function for the fraction (c) of lattice sites in percolating clusters in …

We study the Ising models on the Penrose lattice and the dual Penrose lattice by means of
the high-precision Monte Carlo simulation. Simulating systems up to the total system size N …