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The emergence of collective oscillations and synchronization is a widespread phenomenon in complex systems. While widely studied in dynamical systems theory, this phenomenon is not well understood in the context of out-of-equilibrium phase…
We improved the decoupling approximation of the double-time Green's function theory, and applied it to study the spin-${1\over 2}$ two-dimensional antiferromagnetic Heisenberg model with broken bonds at finite temperature. Our decoupling…
Similarities between fragile glasses and spin glasses (SG) suggest the study of frustrated spin model to understand the complex dynamics of glasses above the glass transition. We consider a frustrated spin model with Ising spins and s-state…
We study the problem of testing and recovering $k$-clique Ferromagnetic mean shift in the planted Sherrington-Kirkpatrick model (i.e., a type of spin glass model) with $n$ spins. The planted SK model -- a stylized mixture of an uncountable…
The classical relationship between the Tutte polynomial of graph theory and the Potts model of statistical mechanics has resulted in valuable interactions between the disciplines. Unfortunately, it does not include the external magnetic…
Combining traditional Wang-Landau sampling for multiple replica systems with an exchange of densities of states between replicas, we describe a general framework for simulations on massively parallel Petaflop supercomputers. The advantages…
The use of combinatorial optimization algorithms has contributed substantially to the major progress that has occurred in recent years in the understanding of the physics of disordered systems, such as the random-field Ising model. While…
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…
In the Ising model, we consider the problem of estimating the covariance of the spins at two specified vertices. In the ferromagnetic case, it is easy to obtain an additive approximation to this covariance by repeatedly sampling from the…
The identification of microscopic models describing the low-energy properties of correlated materials has been a central goal of spectroscopic measurements. We demonstrate how 2D non-linear spectroscopy can be used to distinguish effective…
Low-temperature magnetization curves and thermodynamics of a frustrated spin-1/2 Heisenberg triangular bilayer with the antiferromagnetic intradimer interaction and either ferromagnetic or antiferromagnetic interdimer interaction are…
Interacting quantum spin models are remarkably useful for describing different types of physical, chemical, and biological systems. Significant understanding of their equilibrium properties has been achieved to date, especially for the case…
Error-mitigation methods for Ising machines are reexamined not merely as noise-suppression techniques but as a structural design problem of replica-coupled Ising models. Using simulated annealing as a hardware-noise-free testbed, we…
Hardcore and Ising models are two most important families of two state spin systems in statistic physics. Partition function of spin systems is the center concept in statistic physics which connects microscopic particles and their…
We find the cross-over behavior for the spin-spin correlation function for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation approach of the perturbation series…
We study transverse spin dynamics on a microscopic level by measuring energy-resolved spin correlations in weakly interacting Fermi gases (WIFGs). The trapped cloud behaves as a many-body spin-lattice in energy space with effective…
A feedback vertex set (FVS) of an undirected graph is a set of vertices that contains at least one vertex of each cycle of the graph. The feedback vertex set problem consists of constructing a FVS of size less than a certain given value.…
Computing the partition function, $Z$, of an Ising model over a graph of $N$ \enquote{spins} is most likely exponential in $N$. Efficient variational methods, such as Belief Propagation (BP) and Tree Re-Weighted (TRW) algorithms, compute…
We present an analytic approach to study concurrent influence of quenched non-magnetic site-dilution and finiteness of the lattice on the 2D XY model. Two significant deeply connected features of this spin model are: a special type of…
The finite lattice method of series expansion is generalised to the $q$-state Potts model on the simple cubic lattice. It is found that the computational effort grows exponentially with the square of the number of series terms obtained,…