Laplacian roughening on a triangular lattice

Kosterlitz–Thouless physics: a review of key issues

“…In a series of papers [189][190][191][192][193][194][195][196], Kleinert and coworkers developed and simulated a model for 2D melting including an important additional parameter which allows for first order melting within a theory based on elasticity. By allowing for higher order elastic effects [195] [195]…”

“…However, Kleinert [195,196] has shown that the parameter ′ l 2 is irrelevant for melting and considers only l 2 , which is a measure of rotational stiffness. A model combining both mechanisms leading to first order melting [192] and [86] might be more realistic than existing models.…”

“…The vortex core has radius ( ) ξ O 0 which is the smallest length scale of the system. When = H 0, these considerations lead to the free energy (192) where e * = 2e and = * m m 2 e are the charge and mass of a Cooper pair. To see the effect of the field ( ) z B r, due to a set of vortices in the superconducting plane at z = 0, one follows the analysis of Pearl [237] and Nelson [238] by assuming the superconducting current is only in the z = 0 plane so that (195) which translates into the vortex-vortex interaction behaving as r ln for λ < ⊥ r and as 1/r 2 for λ ⊥ r .…”

“…Thus, one can assume that the temperature T T 0 , the Ginzburg-Landau critical temperature. The system is effectively two dimensional when the film thickness ξ d 0 since we can integrate (189) (192) where e * = 2e and = * m m 2 e are the charge and mass of a Cooper pair. To see the effect of the field ( ) z B r, due to a set of vortices in the superconducting plane at z = 0, one follows the analysis of Pearl [237] and Nelson [238] by assuming the superconducting current is only in the z = 0 plane so that 2 .…”

Single transition of discrete Laplacian roughening model on a square lattice

“…Strandburg et al [35] also studied the LR model on a triangular lattice by the Monte Carlo simulation and showed the existence of an intermediate hexatic phase via the height and slope correlation functions. However, Janke and Kleinert found a single first-order transition with the metastable states in the studies for the LR model on both a square lattice [36] and a triangular lattice [37]. In the later work of Ruiz-Lorenzo et al [38], they studied the LR model on both square and triangular lattices and observed a single transition of the Kosterlitz-Thouless (KT) type possibly [39].…”