arXiv subjects

Ranasinghe P. K. C. Malmini

Publications and source records attributed to Ranasinghe P. K. C. Malmini.

3 recordsLinked to original sources

arXiv2007

The Gonihedric Ising Model and Glassiness

The Gonihedric 3D Ising model is a lattice spin model in which planar Peierls boundaries between + and - spins can be created at zero energy cost. Instead of weighting the area of Peierls boundaries as the case for the usual 3D Ising model with nearest neighbour interactions, the edges, or "bends" in an interface are weighted, a concept which is related to the intrinsic curvature of the boundaries in the continuum. In these notes we follow a roughly chronological order by first reviewing the background to the formulation of the model, before moving on to the elucidation of the equilibrium phase diagram by various means and then to investigation of the non-equilibrium, glassy behaviour of the model.

cond-mat.stat-mech↗

arXiv2002

The Information Geometry of the Ising Model on Planar Random Graphs

It has been suggested that an information geometric view of statistical mechanics in which a metric is introduced onto the space of parameters provides an interesting alternative characterisation of the phase structure, particularly in the case where there are two such parameters -- such as the Ising model with inverse temperature $β$ and external field $h$. In various two parameter calculable models the scalar curvature ${\cal R}$ of the information metric has been found to diverge at the phase transition point $β_c$ and a plausible scaling relation postulated: ${\cal R} \sim |β- β_c|^{α- 2}$. For spin models the necessity of calculating in non-zero field has limited analytic consideration to 1D, mean-field and Bethe lattice Ising models. In this letter we use the solution in field of the Ising model on an ensemble of planar random graphs (where $α=-1, β=1/2, γ=2$) to evaluate the scaling behaviour of the scalar curvature, and find ${\cal R} \sim | β- β_c |^{-2}$. The apparent discrepancy is traced back to the effect of a negative $α$.

cond-mat.stat-mech↗

arXiv1996

Gonihedric 3D Ising Actions

We investigate a generalized Ising action containing nearest neighbour, next to nearest neighbour and plaquette terms that has been suggested as a potential string worldsheet discretization on cubic lattices by Savvidy and Wegner. We use both mean field techniques and Monte-Carlo simulations to sketch out the phase diagram. The Gonihedric (Savvidy-Wegner) model has a symmetry that allows any plane of spins to be flipped with zero energy cost, which gives a highly degenerate vacuum state. We choose boundary conditions in the simulations that eliminate this degeneracy and allow the definition of a simple ferromagnetic order parameter. This in turn allows us to extract the magnetic critical exponents of the system.

hep-lat↗