Subexponentially Growing Hilbert Space and Nonconcentrating Distributions in a Constrained Spin Model

• Published in: Journal of statistical physics Vol. 171; no. 3; pp. 449 - 461
• Main Authors: Webster, Jason R., Kastner, Michael
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2018; Springer; Springer Nature B.V
• Subjects: Analysis; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONCENTRATION RATIO; CONDENSATES; Constraint modelling; DISTRIBUTION; DISTRIBUTION FUNCTIONS; EXPECTATION VALUE; HILBERT SPACE; Mathematical and Computational Physics; ORDER PARAMETERS; PHASE TRANSFORMATIONS; Phase transitions; Physical Chemistry; Physics; Physics and Astronomy; Probability distributions; Quantum Physics; SPIN; Statistical analysis; Statistical Physics and Dynamical Systems; Theoretical; THERMODYNAMIC PROPERTIES; THERMODYNAMICS; Concentration of measure; Fully-connected spin model; Canonical ensemble
• ISSN: 0022-4715; 1572-9613
• DOI: 10.1007/s10955-018-2016-y

Motivated by recent experiments with two-component Bose–Einstein condensates, we study fully-connected spin models subject to an additional constraint. The constraint is responsible for the Hilbert space dimension to scale only linearly with the system size. We discuss the unconventional statistical physical and thermodynamic properties of such a system, in particular the absence of concentration of the underlying probability distributions. As a consequence, expectation values are less suitable to characterize such systems, and full distribution functions are required instead. Sharp signatures of phase transitions do not occur in such a setting, but transitions from singly peaked to doubly peaked distribution functions of an “order parameter” may be present.