arXiv subjects

M. Cassandro

Publications and source records attributed to M. Cassandro.

2 recordsLinked to original sources

arXiv2002

Geometry of contours and Peierls estimates in d=1 Ising models

Following Fröhlich and Spencer, we study one dimensional Ising spin systems with ferromagnetic, long range interactions which decay as $|x-y|^{-2+α}$, $0\leq α\leq 1/2$. We introduce a geometric description of the spin configurations in terms of triangles which play the role of contours and for which we establish Peierls bounds. This in particular yields a direct proof of the well known result by Dyson about phase transitions at low temperatures.

math-ph↗

arXiv1993

Renormalization Group Approach to Interacting Crumpled Surfaces: The hierarchical recursion

We study the scaling limit of a model of a tethered crumpled D-dimensional random surface interacting through an exclusion condition with a fixed impurity in d-dimensional Euclidean space by the methods of Wilson's renormalization group. In this paper we consider a hierarchical version of the model and we prove rigorously the existence of the scaling limit and convergence to a non-Gaussian fixed point for $1 \leq D< 2$ and $ε>0$ sufficiently small, where $ε= D - (2-D) {d\over 2}$.

hep-th↗