Related papers: Interaction Hierarchy
Motivated by experimental progress in the growth of heavy transition metal oxides, we theoretically study a class of lattice models of interacting fermions with strong spin-orbit coupling. Focusing on interactions of intermediate strength,…
The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of…
We suggest a new mean field method for studying the thermodynamic competition between magnetic and superconducting phases in a two-dimensional square lattice. A partition function is constructed by writing microscopic interactions that…
We propose a statistical mechanics approach to a coevolving spin system with an adaptive network of interactions. The dynamics of node states and network connections is driven by both spin configuration and network topology. We consider a…
The article represents a research of the cosmological evolution of fermion statistical systems with fantom scalar interaction where "kinetic" term's contribution to the total energy of a scalar field is negative. As a result of analytical…
The geometrical approach to phase transitions is illustrated by simulating the high-temperature representation of the Ising model on a square lattice.
Motivated by recent interests in fracton topological phases, we explore the interplay between gapped 2D $\mathbb{Z}_N$ topological phases which admit fractional excitations with restricted mobility and geometry of the lattice on which such…
We study the spectral properties of the transfer matrix for a gonihedric random surface model on a three-dimensional lattice. The transfer matrix is indexed by generalized loops in a natural fashion and is invariant under a group of motions…
Spatial many-species predator-prey systems have been shown to yield very rich space-time patterns. This observation begs the question whether there exist universal mechanisms for generating this type of emerging complex patterns in…
The surface states in three-dimensional (3D) topological insulators (TIs) can be described by a two-dimensional (2D) continuous Dirac Hamiltonian. However, there exists the Fermion doubling problem when putting the continuous 2D Dirac…
Here, we analyse two Dirac fermion species in two spatial dimensions in the presence of general quartic contact interactions. By employing functional bosonisation techniques, we demonstrate that depending on the couplings of the fermion…
On the space of $\pm 1$ spin configurations on the 3$d$-square lattice, we consider the \emph{shaken dynamics}, a parallel Markovian dynamics that can be interpreted in terms of Probabilistic Cellular Automata. The transition probabilities…
We develop an analytical formalism to determine the statistical properties of a system consisting of an ensemble of vortices with random position in plane interacting with a turbulent field. We calculate the generating functional by…
We consider the equilibrium dynamics of Ising spin models with multi-spin interactions on sparse random graphs (Bethe lattices). Such models undergo a mean field glass transition upon increasing the graph connectivity or lowering the…
Models that rely solely on pairwise relationships often fail to capture the complete statistical structure of the complex multivariate data found in diverse domains, such as socio-economic, ecological, or biomedical systems. Non-trivial…
We study a spin system with two- and four-spin exchange interactions on the triangular lattice, which is a possible model for the nuclear magnetism of solid $^3$He layers. It is found that a novel spin structure with scalar chiral order…
Systems of strongly interacting particles, fermions or bosons, can give rise to topological phases that are not acessible to non-interacting systems. Many such interaction-enabled topological phases have been discussed theoretically but few…
We perform Monte Carlo simulations of a four-dimensional gauge invariant spin system which describes random surfaces with gonihedric action. We develop the analogy between the flat-crumpled phase transition of the lattice surface model and…
In this work we review some recent development in the mathematical modelling of quantitative sociology by means of statistical mechanics. After a short pedagogical introduction to static and dynamic properties of many body systems, we…
Generative models have advanced significantly in sampling material systems with continuous variables, such as atomistic structures. However, their application to discrete variables, like atom types or spin states, remains underexplored. In…