Related papers: Hierarchical Spherical Model from a Geometric Poin…
In this paper, we study the low temperature limit of the spherical Crisanti-Sommers variational problem. We identify the $\Gamma$-limit of the Crisanti-Sommers functionals, thereby establishing a rigorous variational problem for the ground…
We study scaling behavior in 2D, S=1/2 and S=1 Heisenberg antiferromagnets using the data on full q-dependences of the equal time structure factor and the static susceptibility, calculated through high temperature expansions. We also carry…
This paper aims to study the functional renormalization group for quantum $(2+p)$-spin dynamics of a $N$-vector $\textbf{x}\in \mathbb{R}^N$. By fixing the gauge symmetry in the construction of the FRG, that breaks the $O(N)$-symmetry and…
We study 2D quantum gravity on spherical topologies using the Regge calculus approach with the $dl/l$ measure. Instead of a fixed non-regular triangulation which has been used before, we study for each system size four different random…
We construct a family of integrable vertex model based on the typical four-dimensional representations of the quantum group deformation of the Lie superalgebra $sl(2|1)$. Upon alternation of such a representation with its dual this model…
We consider a quasilinear parabolic differential equation associated with the renormalization group transformation of the two-dimensional hierarchical Coulomb system in the limit as the size of the block L goes to 1. We show that the…
We study renormalization group multicritical fixed points in the $\epsilon$-expansion of scalar field theories characterized by the symmetry of the (hyper)cubic point group $H_N$. After reviewing the algebra of $H_N$-invariant polynomials…
We develop a new renormalization group approach to the large-N limit of matrix models. It has been proposed that a procedure, in which a matrix model of size (N-1) \times (N-1) is obtained by integrating out one row and column of an N…
We explore O(N) models in dimensions $4<d<6$. Specifically, we investigate models of an O(N) vector field coupled to an additional scalar field via a cubic interaction. Recent results in $d=6-\epsilon$ have uncovered an interacting…
We examine the stiffness of the Heisenberg spin-glass (SG) model at both zero temperature (T=0) and finite temperatures ($T \ne 0$) in three dimensions. We calculate the excess energies at T=0 which are gained by rotating and reversing all…
In hep-th/0311177, the Large $N$ renormalization group (RG) flows of a modified matrix quantum mechanics on a circle, capable of capturing effects of nonsingets, were shown to have fixed points with negative specific heat. The corresponding…
We investigated the phase transition behavior of a binary spreading process in two dimensions for different particle diffusion strengths ($D$). We found that $N>2$ cluster mean-field approximations must be considered to get consistent…
We consider a formal discretisation of Euclidean quantum gravity defined by a statistical model of random $3$-regular graphs and making using of the Ollivier curvature, a coarse analogue of the Ricci curvature. Numerical analysis shows that…
A mean field spherical model with random couplings between pairs, quartets, and possibly higher multiplets of spins is considered. It has the same critical behavior as the Sherrington-Kirkpatrick model. It thus exhibits replica symmetry…
The random-field Ising model shows extreme critical slowdown that has been described by activated dynamic scaling: the characteristic time for the relaxation to equilibrium diverges exponentially with the correlation length, $\ln \tau\sim…
According to the standard classification of Conformal Quantum Field Theory (CQFT) in two dimensions, the massless continuum limit of the $O(2)$ model at the Kosterlitz-Thouless (KT) transition point should be given by the massless free…
We study a non linear sigma model $O(N)\otimes O(2)/O(N-2)\otimes O(2)$ describing the phase transition of N-components helimagnets up to two loop order in $D=2+\epsilon$ dimensions. It is shown that a stable fixed point exists as soon as…
We apply the Nozieres-Gallet dynamic renormalization group (RG) scheme to a continuum equilibrium model of a d-dimensional surface relaxing by linear surface tension and linear surface diffusion, and which is subject to a lattice potential…
Four-dimensional state space geometry is worked out for the exactly solved one-dimensional spin-3/2 lattice with a Blume-Emery-Griffiths (BEG) Hamiltonian as well as a more general one with a term containing a non-zero field coupling to the…
The spin-1/2 quantum Heisenberg model is studied in all spatial dimensions d by renormalization-group theory. Strongly asymmetric phase diagrams in temperature and antiferromagnetic bond probability p are obtained in dimensions d \geq 3.…