Related papers: Why Loops Don't Matter
A relation between a class of stationary points of the energy landscape of continuous spin models on a lattice and the configurations of a Ising model defined on the same lattice suggests an approximate expression for the microcanonical…
We study classical Ising spin-$\frac{1}{2}$ models on the 2D square lattice with ferromagnetic or antiferromagnetic nearest-neighbor interactions, under the effect of a pure imaginary magnetic field. The complex Boltzmann weights of spin…
We apply for the first time a new one-loop topological expansion around the Bethe solution to the spin-glass model with field in the high connectivity limit, following the methodological scheme proposed in a recent work. The results are…
The statics of the Fredrickson-Andersen model (FAM) of the liquid-glass transition is solved on the Bethe lattice (BL). The kinetic constraints of the FAM imply on the BL an ergodicity-breaking transition to a (glassy) phase where a…
We quantize the regularity properties of classical graphs that determine spin models for singly-generated Yang-Baxter planar algebras, including the Kauffman polynomial, and construct explicit examples. A source of examples comes from…
We revisit classical bounds of M. E. Fisher on the ferromagnetic Ising model, and show how to efficiently use them on an arbitrary given graph to rigorously upper-bound the partition function, magnetizations, and correlations. The results…
A relation between the average length of loops and their free energy is obtained for a variety of O(n)-type models on two-dimensional lattices, by extending to finite temperatures a calculation due to Kast. We show that the (number)…
We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of q-state spins on arbitrary graphs, to problems in quantum physics. More precisely, we show how to express partition functions as…
This paper develops results for the next nearest neighbour Ising model on random graphs. Besides being an essential ingredient in classic models for frustrated systems, second neighbour interactions interactions arise naturally in several…
The rounding of first order phase transitions by quenched randomness is stated in a form which is applicable to both classical and quantum systems: The free energy, as well as the ground state energy, of a spin system on a $d$-dimensional…
In this paper we investigate an integrable loop model and its connection with a supersymmetric spin chain. The Bethe Ansatz solution allows us to study some properties of the ground state. When the loop fugacity $q$ lies in the physical…
We discuss the use of a ferromagnetic spin model on a random graph to model granular compaction. A multi-spin interaction is used to capture the competition between local and global satisfaction of constraints characteristic for geometric…
We consider the pyrochlore-lattice quantum Heisenberg ferromagnet and discuss the properties of this spin model at arbitrary temperatures. To this end, we use the Green's function technique within the random-phase (or Tyablikov)…
We introduce a lattice model for a classical doped two dimensional antiferromagnet which has no quenched disorder, yet displays slow dynamics similar to those observed in supercooled liquids. We calculate two-time spatial and spin…
Statistical physics models with hard constraints, such as the discrete hard-core gas model (random independent sets in a graph), are inherently combinatorial and present the discrete mathematician with a relatively comfortable setting for…
We study the interaction corrections to the transport coefficients in open quantum dots (i.e. dots connected to leads of large conductance $G \gg e^2/\pi\hbar$), via a quantum kinetic equation approach. The effects of all the channels of…
We defined exponential maps with one parameter, associated with geodesics on the parameter surface. By group theory we proposed a formula of the critical points, which is a direct sum of the Lie subalgebras at the critical temperature. We…
We study spin-1/2 fermions in spin dependent potentials under the \emph{spin model approximation}, in which interatomic collisions that change the total occupation of single-particle modes are ignored. The spin model approximation maps the…
We consider the Ising model on the Bethe lattice with aperiodic modulation of the couplings, which has been studied numerically in Phys. Rev. E 77, 041113 (2008). Here we present a relevance-irrelevance criterion and solve the critical…
The search for departures from standard hydrodynamics in many-body systems has yielded a number of promising leads, especially in low dimension. Here we study one of the simplest classical interacting lattice models, the nearest-neighbour…