Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2407.13827

A novel translationally invariant supersymmetric chain with inverse-square interactions: partition function, thermodynamics and criticality

Bireswar Basu-Mallick·Federico Finkel·Artemio González-López
View original source ↗Read source document ↗Export metadata ↓

Abstract

We introduce a novel family of translationally-invariant su$(m|n)$ supersymmetric spin chains with long-range interaction not directly associated to a root system. We study the symmetries of these models, establishing in particular the existence of a boson-fermion duality characteristic of this type of systems. Taking advantage of the relation of the new chains with an associated many-body supersymmetric spin dynamical model, we are able to compute their partition function in closed form for all values of $m$ and $n$ and for an arbitrary number of spins. When both $m$ and $n$ are even, we show that the partition function factorizes as the product of the partition functions of two supersymmetric Haldane-Shastry spin chains, which in turn leads to a simple expression for the thermodynamic free energy per spin in terms of the Perron eigenvalue of a suitable transfer matrix. We use this expression to study the thermodynamics of a large class of these chains, showing in particular that the specific heat presents a single Schottky peak at approximately the same temperature as a suitable $k$-level model. We also analyze the critical behavior of the new chains, and in particular the ground state degeneracy and the existence of low energy excitations with a linear energy-momentum dispersion relation. In this way we are able to show that the only possible critical chains are the ones with $m=0,1,2$. In addition, using the explicit formula for the partition function we are able to establish the criticality of the su$(0|n)$ and su$(2|n)$ chains with even $n$, and to evaluate the central charge of their associated conformal field theory.

Explore related subjects

cond-mat.stat-mechmath-phmath.MPnlin.SIquant-ph

Keep this discovery

BibTeXRIS

Bireswar Basu-Mallick, Federico Finkel, Artemio González-López. 2024-07-18. A novel translationally invariant supersymmetric chain with inverse-square interactions: partition function, thermodynamics and criticality. https://arxiv.org/abs/2407.13827

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Universal sampling of spin systems across quenched disorder

Statistical physics extracts macroscopic laws by averaging over the many microscopic degrees of freedom of a system. Disordered systems demand a second and far harder average, one over the quenched randomness itself. The classic analytical routes, the replica and cavity methods, become uncontrolled outside mean-field or tree-like limits, and conventional numerical algorithms like parallel tempering require expensive, independent equilibration for every disorder realization. In this work, we introduce a universal neural variational framework that amortizes inference across the disorder ensemble, eliminating both the need for per-instance Markov chain equilibration and the cost of retraining instance-specific variational ansatzes. Built on an encoder-decoder Transformer architecture, after training once, it produces an explicit approximation to the Boltzmann distribution given previously unseen disorder realizations without further optimization. We validate this framework on 2D Edwards-Anderson models, and apply it to the random-bond Ising model, successfully capturing the Binder cumulant crossings near the Nishimori multicritical point. These results shift the object of variational inference from the single instance to the disorder ensemble, opening a route to frustrated many-body systems where instance-by-instance computation is prohibitive.

cond-mat.stat-mech↗
arXiv2026

Information-Theoretic Characterization of Macroscopic Chaos Emerging from the Chemical Master Equation

Open chemical reaction networks exhibit stochastic concentration dynamics at finite system sizes, whereas their macroscopic limit is governed by deterministic rate equations that can display chaos. In this Letter, we show theoretically that a rate of information loss constructed from two-time mutual information recovers the Kolmogorov-Sinai entropy in the deterministic limit. We verify this result through numerical simulations of a Markov jump process for a three-species system involving seven reactions.

cond-mat.stat-mech↗
arXiv2026

Orientational order on non-orientable domains

We study the statistical properties of passive and active many-body systems with orientational degrees of freedom on non-orientable domains. By rephrasing topological constraints as non-local symmetry relations on an orientable double-cover, we show that non-orientability eliminates global rotational soft modes without acting like an external field. In a passive XY model, this results in topological caging, where orientational fluctuations that exhibit conventional diffusive behavior on a torus saturate on a Klein bottle to a finite value that we compute exactly in the thermodynamic limit. In models of active self-propelled particles with orientational degrees of freedom, topological caging persists despite continuously changing interaction neighborhoods. In an active Ising spin model, non-orientability enforces the coexistence of ordered anti-parallel domains with vanishing global polar order, a state that is absent on orientable domains.

cond-mat.stat-mech↗