Related papers: The inverse Mermin-Wagner theorem for classical sp…
We prove that at any inverse temperature $\beta$ and on any transitive amenable graph, the automorphism-invariant Gibbs states of the ferromagnetic Ising model are convex combinations of the plus and minus states. This is obtained for a…
Spontaneous symmetry breaking phenomena in the transverse field mixed $p$-spin glass model in finite dimensions are studied with Nishimori's gauge theory. Useful identities in the gauge theory enable us to study $\mathbb Z_2$-symmetry…
We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared with the total number of edges. This extends the recent…
This paper is the second in a series of papers considering symmetry properties of a bosonic quantum system over an 2D graph, with continuous spins, in the spirit of the Mermin--Wagner theorem. Here we consider bosonic systems on…
The main goal of the paper is to prove central limit theorems for the magnetization rescaled by $\sqrt{N}$ for the Ising model on random graphs with $N$ vertices. Both random quenched and averaged quenched measures are considered. We work…
We develop a mean-field theory for random quantum spin systems using the spin coherent state path integral representation. After the model is reduced to the mean field one-body Hamiltonian, the integral is analyzed with the aid of several…
We predict that the magnetization direction of a ferromagnet can be reversed by the spin-transfer torque accompanying spin-polarized thermoelectric heat currents. We illustrate the concept by applying a finite-element theory of…
We examine n component spin systems with arbitrary two spin interactions (of unspecified range) within a general framework to highlight some new subtleties present in incommensurate systems. We determine the ground states of all…
We prove that the q-states Potts model on graph is spontaneously magnetized at finite temperature if and only if the graph presents percolation on the average. Percolation on the average is a combinatorial problem defined by averaging over…
The origin of thermal and quantum entanglement in a class of three-dimensional spin models, at low momenta, is traced to purely topological reasons. The establishment of the result is facilitated by the gauge principle which, when used in…
We study the inverse problem of determining a finite weighted graph $(X,E)$ from the source-to-solution map on a vertex subset $B\subset X$ for heat equations on graphs, where the time variable can be either discrete or continuous. We prove…
We use the Boltzmann transport theory in the relaxation time approximation to describe the thermal transport of spin waves in a ferromagnet. By treating spin waves as magnon excitations we are able to compute analytically and numerically…
We theoretically and numerically investigate spin waves that occur in systems of classical magnetic dipoles that are arranged at the vertices of a regular polygon and interact solely via their magnetic fields. There are certain limiting…
The Hohenberg--Mermin--Wagner theorem states that there is no spontaneous breaking of continuous symmetries in spatial dimensions $d\leq2$ at finite temperature. At zero temperature, the classical/quantum mapping further implies the absence…
We check the existence of a spontaneous magnetisation of Ising and Potts spins on semi-directed Barabasi-Albert networks by Monte Carlo simulations. We verified that the magnetisation for different temperatures $T$ decays after a…
With up to 7 million spins, the existence of spontaneous magnetization of Ising spins on directed Barabasi-Albert networks is investigated by Monte Carlo simulations. We confirm our earlier result that the magnetization for different…
A spin model that displays inverse melting and inverse glass transition is presented and analyzed. Strong degeneracy of the interacting states of an individual spin leads to entropic preference of the "ferromagnetic" phase, while lower…
This paper deals with the stochastic Ising model with a temperature shrinking to zero as time goes to infinity. A generalization of the Glauber dynamics is considered, on the basis of the existence of simultaneous flips of some spins. Such…
While classical spin systems in random networks have been intensively studied, much less is known about quantum magnets in random graphs. Here, we investigate interacting quantum spins on small-world networks, building on mean-field theory…
It is a classical result of Wigner that for an hermitian matrix with independent entries on and above the diagonal, the mean empirical eigenvalue distribution converges weakly to the semicircle law as matrix size tends to infinity. In this…