Related papers: Spin models from nonlinear cellular automata
Some models allowing explicit calculation of periodic instantons and evaluation of their action are studied with regard to transitions from classical to quantum behaviour as the temperature is lowered and tunneling sets in. It is shown that…
The investigation of the behavior of both classical and quantum systems on non-Euclidean surfaces near the phase transition point represents an interesting research area of modern physics. In the case of classical spin systems, a…
We consider the group structure of quantum cellular automata (QCA) modulo circuits and show that it is abelian even without assuming the presence of ancillas, at least for most reasonable choices of control space; this is a corollary of a…
Recent advances on quantum foundations achieved the derivation of free quantum field theory from general principles, without referring to mechanical notions and relativistic invariance. From the aforementioned principles a quantum cellular…
We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped…
We introduce and describe a class of simple facilitated quantum spin models in which the dynamics is due to the repeated application of unitary gates. The gates are applied periodically in time, so their combined action constitutes a…
We consider two limiting regimes, the large-spin and the mean-field limit, for the dynamical evolution of quantum spin systems. We prove that, in these limits, the time evolution of a class of quantum spin systems is determined by a…
We consider the Blume-Capel model with the quantum tunneling between the excited states. We find a magnetically ordered phase transition induced by quantum fluctuation in a model. The model has no phase transition in the corresponding…
The goal of this work is to build a dynamical theory of defects for quantum spin systems. A kinematic theory for an indefinite number of defects is first introduced exploiting distinguishable Fock space. Dynamics are then incorporated by…
Formation of chaos in the parametric dependent system of interacting oscillators for the both classical and quantum cases has been investigated. Domain in which classical motion is chaotic is defined. It has been shown that for certain…
Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on higher dimensional CA and aims at showing that the situation is different…
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…
It has been shown that certain quantum walks give rise to relativistic wave equations, such as the Dirac and Weyl equations, in their long-wavelength limits. This intriguing result raises the question of whether something similar can happen…
We investigate the spin dynamics of a dipole-coupled system by comparing a direct solution of the Schrodinger equation for quantum spins with simulations of classical spins. Although classical spins have long been used in microscopic spin…
We use the multiscale entanglement renormalisation ansatz (MERA) to numerically investigate three critical quantum spin chains with Z_2 x Z_2 on-site symmetry: a staggered XXZ model, a transverse field cluster model, and the quantum…
The rounding of first order phase transitions by quenched randomness is stated in a form which is applicable to both classical and quantum systems: The free energy, as well as the ground state energy, of a spin system on a $d$-dimensional…
A nonlinear model of the scalar field with a coupling between the field and its gradient is developed. It is shown, that such model is suitable for the description of phase transition accompanied by formation of spatial inhomogeneous…
Cellular automata can show well known features of quantum mechanics, such as a linear updating rule that resembles a discretized form of the Schr\"odinger equation together with its conservation laws. Surprisingly, a whole class of…
Probabilistic cellular automata (CA) provides a classic framework for studying non-equilibrium statistical physics on a lattices. A notable example is the Domany-Kinzel CA, which has been used to investigate the process of directed…
In this short note we study Spin-Boson Models from the Quasi-Classical standpoint. In the Quasi-Classical limit, the field becomes macroscopic while the particles it interacts with, they remain quantum. As a result, the field becomes a…