Related papers: Exact matrix model for generalized Ising model
Recent work on random field Ising model is described briefly emphasizing exact solutions of the model in simple cases and their relevance in understanding equilibrium and non-equilibrium properties of systems with quenched disorder.
The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters…
A one-dimensional Ising model with nearest neighbour interactions is applied to study compaction processes in granular media. An equivalent particle-hole picture is introduced, with the holes being associated to the domain walls of the…
We present a general class of machine learning algorithms called parametric matrix models. In contrast with most existing machine learning models that imitate the biology of neurons, parametric matrix models use matrix equations that…
The current understanding of aging phenomena is mainly confined to the study of systems with short-ranged interactions. Little is known about the aging of long-ranged systems. Here, the aging in the phase-ordering kinetics of the…
One-dimensional systems---ranging from travelling light to circuit cables and from DNA to superstrings---are ubiquitous and critically important to the human knowledge of the universe. However, our engagement with one-dimensional systems in…
We review some aspects of the fermionic interpretation of the two-dimensional Ising model. The use is made of the notion of the integral over the anticommuting Grassmann variables. For simple and more complicated 2D Ising lattices, the…
Motivated by recent interest in 2+1 dimensional quantum dimer models, we revisit Fisher's mapping of two dimensional Ising models to hardcore dimer models. First, we note that the symmetry breaking transition of the ferromagetic Ising model…
A common issue when analyzing real-world complex systems is that the interactions between the elements often change over time: this makes it difficult to find optimal models that describe this evolution and that can be estimated from data,…
Hierarchical spin-glasses are Ising spin models defined by recursively coupling together two equally-sized sub-systems. In this work a new hierarchical spin system is introduced wherein the sub-systems are recursively coupled together…
The s=3/2 Ising spin chain with uniform nearest-neighbor coupling, quadratic single-site potential, and magnetic field is shown to be equivalent to a system of 17 species of particles with internal structure. The same set of particles (with…
Finite size effects for the Ising Model coupled to two dimensional random surfaces are studied by exploiting the exact results from the 2-matrix models. The fixed area partition function is numerically calculated with arbitrary precision by…
We introduce a model for describing the dynamics of large numbers of interacting cells. The fundamental dynamical variables in the model are sub-cellular elements, which interact with each other through phenomenological intra- and…
Dynamical Ising machines are continuous dynamical systems that evolve from a generic initial state to a state strongly related to the ground state of the classical Ising model. We show that such a machine driven by the V${}_2$ dynamical…
Since its foundations, more than one hundred years ago, the field of structural biology has strived to understand and analyze the properties of molecules and their interactions by studying the structure that they take in 3D space. However,…
Now that spike trains from many neurons can be recorded simultaneously, there is a need for methods to decode these data to learn about the networks that these neurons are part of. One approach to this problem is to adjust the parameters of…
Studying systems where many individual bodies in motion interact with one another is a complex and interesting area. Simple mechanisms that may be determined for biological, chemical, or physical reasons can lead to astonishingly complex…
Transfer-matrix methods, with the help of finite-size scaling and conformal invariance concepts, are used to investigate the critical behavior of two-dimensional square-lattice Ising spin-1/2 systems with first- and second-neighbor…
A systematic study of both classical and quantum geometric frustrated Ising models with a competing ordering mechanism is reported in this paper. The ordering comes in the classical case from a coupling of 2D layers and in the quantum model…
We consider the Ising model and the directed walk on two-dimensional layered lattices and show that the two problems are inherently related: The zero-field thermodynamical properties of the Ising model are contained in the spectrum of the…