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We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of…
Market Mill is a complex dependence pattern leading to nonlinear correlations and predictability in intraday dynamics of stock prices. The present paper puts together previous efforts to build a dynamical model reflecting the market mill…
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…
We study a Hamiltonian system describing a three-spin-1/2 cluster-like interaction competing with an Ising-like anti-ferromagnetic interaction. We compute free energy, spin correlation functions and entanglement both in the ground and in…
We investigate Ising model description of dynamics of stock price. The model is defined in near 2 dimensions, one dimension is time and another represents ensemble of stocks, and strength of response of investors to price change corresponds…
Spin models of markets inspired by physics models of magnetism, as the Ising model, allow for the study of the collective dynamics of interacting agents in a market. The number of possible states has been mostly limited to two (buy or sell)…
The dynamics of a localized molecular spin under the influence of external voltage pulses is addressed using a generalized spin equation of motion. The approach incorporates anisotropic fields, non-equilibrium conditions, and non-adiabatic…
A kinetic Ising model is analyzed where spin variables correspond to lattice cells with mobile or immobile particles. Introducing additional restrictions for the flip processes according to the n-spin facilitated kinetic Ising model and…
We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…
Nonreciprocal interactions in many-body systems lead to time-dependent states, commonly observed in biological, chemical, and ecological systems. The stability of these states in the thermodynamic limit and the critical behavior of the…
We attempt to explain stock market dynamics in terms of the interaction among three variables: market price, investor opinion and information flow. We propose a framework for such interaction and apply it to build a model of stock market…
It is widely accepted that the dynamic of entanglement in presence of a generic circuit can be predicted by the knowledge of the statistical properties of the entanglement spectrum. We tested this assumption by applying a Metropolis-like…
Using rigorous analytical analysis and exact numerical data for the spin-1/2 transverse Ising chain we discuss the effects of regular alternation of the Hamiltonian parameters on the quantum phase transition inherent in the model.
The Glauber model on a one-dimensional lattice with boundaries (for the ferromagnetic- and anti-ferromagnetic case) is considered. The large-time behaviour of the one-point function is studied. It is shown that, for any positive…
We analyze a non-Markovian mean field interacting spin system, related to the Curie--Weiss model. We relax the Markovianity assumption by replacing the memoryless distribution of the waiting times of a classical spin-flip dynamics with a…
The purpose of this article is to present a detailed numerical study of the second-order phase transition in the 2D Ising model. The importance of correctly presenting elementary theory of phase transitions, computational algorithms and…
The agent-based model of stock price dynamics on a directed evolving complex network is suggested and studied by direct simulation. The stationary regime is maintained as a result of the balance between the extremal dynamics, adaptivity of…
The S=1/2, nearest-neighbor, kinetic Ising model has been used to model magnetization switching in nanoscale ferromagnets. For this model, earlier work based on the droplet theory of the decay of metastable phases and Monte Carlo…
In this dissertation two simple models of stock exchange are developed and simulated numerically. The first is characterized by centralized trading with a market maker. Unfortunately, this model is unable to generate realistic market…
A microscopic model of financial markets is considered, consisting of many interacting agents (spins) with global coupling and discrete-time thermal bath dynamics, similar to random Ising systems. The interactions between agents change…