Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userClassical lattice spin models involving singular interactions isotropic in spin space
131
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We address here a few classical lattice--spin models, involving $n-$component unit vectors ($n=2,3$), associated with a $D-$dimensional lattice $mathbb{Z}^D,,D=1,2$, and interacting via a pair potential restricted to nearest neighbours and being isotropic in spin space, i.e. defined by a function of the scalar product between the interacting spins. When the potential involves a continuous function of the scalar product, the Mermin--Wagner theorem and its generalizations exclude orientational order at all finite temperatures in the thermodynamic limit, and exclude phase transitions at finite temperatures when $D=1$; on the other hand, we have considered here some comparatively simple functions of the scalar product which are bounded from below, diverge to $+infty$ for certain mutual orientations, and are continuous almost everywhere with integrable singularities. Exact solutions are presented for $D=1$, showing absence of phase transitions and absence of orientational order at all finite temperatures in the thermodynamic limit; for $D=2$, and in the absence of more stringent mathematical results, extensive simulations carried out on some of them point to the absence of orientational order at all finite temperatures, and suggest the existence of a Berezinskivi-Kosterlitz-Thouless transition.
rate research
Read More
The present paper considers some classical ferromagnetic lattice--gas models, consisting of particles that carry $n$--component spins ($n=2,3$) and associated with a $D$--dimensional lattice ($D=2,3$); each site can host one particle at most, thus implicitly allowing for hard--core repulsion; the pair interaction, restricted to nearest neighbors, is ferromagnetic, and site occupation is also controlled by the chemical potential $mu$. The models had previously been investigated by Mean Field and Two--Site Cluster treatments (when D=3), as well as Grand--Canonical Monte Carlo simulation in the case $mu=0$, for both D=2 and D=3; the obtained results showed the same kind of critical behaviour as the one known for their saturated lattice counterparts, corresponding to one particle per site. Here we addressed by Grand--Canonical Monte Carlo simulation the case where the chemical potential is negative and sufficiently large in magnitude; the value $mu=-D/2$ was chosen for each of the four previously investigated counterparts, together with $mu=-3D/4$ in an additional instance. We mostly found evidence of first order transitions, both for D=2 and D=3, and quantitatively characterized their behaviour. Comparisons are also made with recent experimental results.
We construct models hosting classical fractal spin liquids on two realistic three-dimensional (3D) lattices of corner-sharing triangles: trillium and hyperhyperkagome (HHK). Both models involve the same form of three-spin Ising interactions on triangular plaquettes as the Newman-Moore (NM) model on the 2D triangular lattice. However, in contrast to the NM model and its 3D generalizations, their degenerate ground states and low-lying excitations cannot be described in terms of scalar cellular automata (CA), because the corresponding fractal structures lack a simplifying algebraic property, often termed the Freshmans dream. By identifying a link to matrix CAs -- that makes essential use of the crystallographic structure -- we show that both models exhibit fractal symmetries of a distinct class to the NM-type models. We devise a procedure to explicitly construct low-energy excitations consisting of finite sets of immobile defects or fractons, by flipping arbitrarily large self-similar subsets of spins, whose fractal dimensions we compute analytically. We show that these excitations are associated with energetic barriers which increase logarithmically with system size, leading to fragile glassy dynamics, whose existence we confirm via classical Monte Carlo simulations. We also discuss consequences for spontaneous fractal symmetry breaking when quantum fluctuations are introduced by a transverse magnetic field, and propose multi-spin correlation function diagnostics for such transitions. Our findings suggest that matrix CAs may provide a fruitful route to identifying fractal symmetries and fracton-like behaviour in lattice models, with possible implications for the study of fracton topological order.
We apply the event-chain Monte Carlo algorithm to classical continuum spin models on a lattice and clarify the condition for its validity. In the two-dimensional XY model, it outperforms the local Monte Carlo algorithm by two orders of magnitude, although it remains slower than the Wolff cluster algorithm. In the three-dimensional XY spin glass at low temperature, the event-chain algorithm is far superior to the other algorithms.
This work aims at the goal whether the artificial intelligence can recognize phase transition without the prior human knowledge. If this becomes successful, it can be applied to, for instance, analyze data from quantum simulation of unsolved physical models. Toward this goal, we first need to apply the machine learning algorithm to well-understood models and see whether the outputs are consistent with our prior knowledge, which serves as the benchmark of this approach. In this work, we feed the compute with data generated by the classical Monte Carlo simulation for the XY model in frustrated triangular and union jack lattices, which has two order parameters and exhibits two phase transitions. We show that the outputs of the principle component analysis agree very well with our understanding of different orders in different phases, and the temperature dependences of the major components detect the nature and the locations of the phase transitions. Our work offers promise for using machine learning techniques to study sophisticated statistical models, and our results can be further improved by using principle component analysis with kernel tricks and the neural network method.
Ultra-cold alkali atoms trapped in two distinct hyperfine states in an external magnetic field can mimic magnetic systems of spin 1/2 particles. We describe the spin-dependent effective interaction as a spin-spin interaction. As a consequence of the zero-range, the interaction of spin 1/2 bosons can be described as an Ising or, alternatively, as an XY-coupling. We calculated the spin-spin interaction parameters as a function of the external magnetic field in the Degenerate Internal State (DIS) approximation. We illustrate the advantage of the spin-spin interaction form by mapping the system of N spin 1/2 bosons confined by a tight trapping potential on that of N spin 1/2 spins coupled via an infinite range interaction.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
