Evidence for a first order transition in a plaquette 3 d Ising-like action

Content Provider	Semantic Scholar
Author	Baig, M. Shakeel Johnston, Desmond A. Malmini, Ranasinghe P. K. C.
Copyright Year	2008
Abstract	We investigate a 3d Ising action which corresponds to a a class of models defined by Savvidy and Wegner, originally intended as discrete versions of string theories on cubic lattices. These models have vanishing bare surface tension and the couplings are tuned in such a way that the action depends only on the angles of the discrete surface, i.e. on the way the surface is embedded in Z. Hence the name gonihedric by which they are known. We show that the model displays a rather clear first order phase transition in the limit where self-avoidance is neglected and the action becomes a plaquette one. This transition persists for small values of the self avoidance coupling, but it turns to second order when this latter parameter is further increased. These results exclude the use of this type of action as models of gonihedric random surfaces, at least in the limit where self avoidance is neglected. (a) Permanent Address: Department of Mathematics University of Sri Jayewardenepura Gangodawila, Sri Lanka. In three dimensions the Ising model can be thought of as describing volumes of negative spins in a sea of positive ones, or viceversa. It is well known that the familiar Ising action weights such configurations according to the number of ‘broken’ links, i.e. with an action which is approximately proportional to the area of such volumes. Apart from entropy effects, the energy of a given configuration depends only on the surface, thus leading to a non-zero bare surface tension, but it is independent of the ‘form’ of the surface, i.e. of the precise way the surface is embedded in the lattice. A rough surface weighs exactly the same as a smooth one as long as the area is the same. Is it possible to define a Ising-like action where precisely the opposite situation takes place? That is, is it possible to assign weights to a Ising action in such a way that smooth surfaces are preferred? The extreme case of such a situation would be one where the bare surface tension would be zero and, if, at all, a renormalized surface tension would be generated by fluctuations. Savvidy et al. [1] recently answered the above question in the positive. They started by suggesting a a novel discretized random surface theory, the so-called gonihedric string, whose action is
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://arxiv.org/pdf/hep-lat/9607002v1.pdf
Language	English
Access Restriction	Open
Subject Keyword	Arabic numeral 0 Coupling (computer programming) Cubic function Discretization Embedded system Embedding Ising model Phase Transition Population Parameter Surface Tension Theory Version Weight
Content Type	Text
Resource Type	Article