Related papers: Interaction Hierarchy
We present a theoretical framework and a calculational scheme to study the coexistence and competition of thermodynamic phases in quantum statistical mechanics. The crux of the method is the realization that the microscopic Hamiltonian,…
Motivated by the recent interest in non-equilibrium phenomena in quantum many-body systems, we study strongly interacting fermions on a lattice by deriving and numerically solving quantum Boltzmann equations that describe their relaxation…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
We perform large scale simulations of the frustrated Ising lattice gas, a three-dimensional lattice model of a structural glass, using the parallel tempering technique. We evaluate the spin and density overlap distributions, and the…
We study the structure of pairing order parameter for spin-1/2 fermions with attractive interactions in a square lattice under a uniform magnetic field. Because the magnetic translation symmetry gives a unique degeneracy in the…
We study multilevel fermions in an optical lattice described by the Hubbard model with on site SU($n$)-symmetric interactions. We show that in an appropriate parameter regime this system can be mapped onto a spin model with all-to-all…
We present an algebraic framework for interacting extended quantum systems to study complex phenomena characterized by the coexistence and competition of different states of matter. We start by showing how to connect different…
All ground states and low-lying excitations of a +/- I Ising spin glass model on a cubic 4 x 4 x 4 lattice with periodical boundary conditions were calculated using a method of combinatorical optimization. The structure of states in the…
We propose a thermodynamic multi-state spin model in order to describe equilibrial behavior of a society. Our model is inspired by the Axelrod model used in social network studies. In the framework of the statistical mechanics language, we…
We review recent results on lattice models for spin-less fermions with strong repulsive interactions. A judicious tuning of kinetic and interaction terms leads to a model possessing supersymmetry. In the 1D case, this model displays…
We present a {\it numerically exact} study of the Hubbard model with spin-dependent anisotropic hopping on the square lattice using auxiliary-field quantum Monte Carlo method. At half filling, the system undergoes Ising phase transitions…
The spin-1 quantum Ising systems with three-spin interactions on two-dimensional triangular lattices are studied by mean-field method. The thermal variations of order parameters and phase diagrams are investigated in detail. The stable,…
This chapter explores dynamical structural equation models (DSEMs) and their nonlinear generalizations into sheaves of dynamical systems. It demonstrates these two disciplines on part of the food web in the Bering Sea. The translation from…
We construct and analyse a dual model to the Ising model with the nearest and next-nearest neighbors on the rectangular lattice (NNNI model). The Hamiltonian of the dual model turns out to contain two- and four-spin interactions. The free…
Ising model with quenched random magnetic fields is examined for single Gaussian, bimodal and double Gaussian random field distributions by introducing an effective field approximation that takes into account the correlations between…
We apply a new anticommuting path integral technique to clarify the fermionic structure of the 2D Ising model with quenched site dilution. In the $N$-replica scheme, the model is explicitly reformulated as a theory of interacting fermions…
We study the magnetic properties of a mixed Ising ferrimagnetic system, in which the two interacting sublattices have spins $\sigma$, $(\pm 1/2)$ and spins $S$, $(\pm 3/2,\pm 1/2)$ in the presence of a random crystal field, with the mean…
We suggest that if a localized phase at nonzero temperature $T>0$ exists for strongly disordered and weakly interacting electrons, as recently argued, it will also occur when both disorder and interactions are strong and $T$ is very high.…
We generalize the recently introduced dual fermion (DF) formalism for disordered fermion systems by including the effect of interactions. For an interacting disordered system the contributions to the full vertex function have to be…
We connect an appropriate feedback loop to a model of 2D vertical eddy of airflow which unfolds a wide range of vorticity behavior. Computational fluid dynamics of the twisted roll display a class of long lifespan 3D vortices. On the one…