Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0810.5539

Criticality in multicomponent spherical models : results and cautions

Jean-Noël Aqua·Michael E. Fisher
View original source ↗Read source document ↗Export metadata ↓

Abstract

To enable the study of criticality in multicomponent fluids, the standard spherical model is generalized to describe an $\ns$-species hard core lattice gas. On introducing $\ns$ spherical constraints, the free energy may be expressed generally in terms of an $\ns\times\ns$ matrix describing the species interactions. For binary systems, thermodynamic properties have simple expressions, while all the pair correlation functions are combinations of just two eigenmodes. When only hard-core and short-range overall attractive interactions are present, a choice of variables relates the behavior to that of one-component systems. Criticality occurs on a locus terminating a coexistence surface; however, except at some special points, an unexpected ``demagnetization effect'' suppresses the normal divergence of susceptibilities at criticality and distorts two-phase coexistence. This effect, unphysical for fluids, arises from a general lack of symmetry and from the vectorial and multicomponent character of the spherical model. Its origin can be understood via a mean-field treatment of an XY spin system below criticality.

Explore related subjects

cond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jean-Noël Aqua, Michael E. Fisher. 2008-10-30. Criticality in multicomponent spherical models : results and cautions. https://doi.org/10.1103/physreve.79.011118

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

KEEP EXPLORING

Related papers

arXiv2026

Sharp Bounds on the Mean Efficiency of a Fluctuating Machine

The efficiency of a machine at the scale of thermal fluctuations is random, and the conventional ratio $-W/Q_h$ has no moment of any order: its input heat fluctuates through zero. We work instead with the exergetic ratio $η=W/(W+T_0S)$, which lies in $[0,1]$ pointwise for non-negative dissipation, and ask what the energy budget alone determines about its mean. With $α=T_0\langle S\rangle/W$ and $σ^2$ the relative variance of the dissipation, $1/(1+α)<\langleη\rangle\leσ^2/(1+σ^2)+1/\{(1+σ^2)[1+α(1+σ^2)]\}$, both ends sharp, with no distributional assumption. The floor is Jensen's inequality: fluctuating dissipation raises the mean efficiency above its deterministic value, and the mean alone gives nothing more. The ceiling is attained by an intermittently reversible law, dissipating nothing in a fraction $σ^2/(1+σ^2)$ of realisations, a prediction testable on trajectories. A third moment lifts the floor. Fixed delivered work is not required: when it too fluctuates, the bounds hold with the moments taken on $T_0S/W$, and the thermodynamic uncertainty relation on the work current converts the ceiling into a precision-efficiency frontier, whose zero-variance member is the known bound on a motor's ratio-of-means efficiency, shown here to be unsafe for the mean of the fluctuating ratio. Inside the interval lies the maximum-entropy benchmark $α^{-1}e^{1/α}E_1(1/α)$. Finally the bounds are worked out for a motor with futile cycles, observed until a fixed number of steps is delivered. There the dissipation cannot fall below the reversible cost of that work, and this floor $b$ sharpens the ceiling to $q/(1+αb)+(1-q)/(1+αc)$, $q=σ^2/[σ^2+(1-b)^2]$, $c=1+σ^2/(1-b)$, removing 40-67 per cent of the width. It is saturated when slips are rare: the extremal law is an operating regime, not an idealisation.

cond-mat.stat-mech↗
arXiv2026

Amplified Memory and Finite-Time Regularity in Driven Non-Hermitian Systems

We study the roles of broken spectra and exceptional points in finite-time driven non-Hermitian fermionic dynamics. We compute the Nambu biorthogonal correlation matrix for this purpose. The imbalanced-pairing Kitaev chain serves as our concrete realization. Transient passage through a broken-spectrum region amplifies preparation memory. The effect survives when the final Hamiltonian returns to a real-spectrum regime. Negative imbalance forces spectral nonpositivity in the static endpoint state. We isolate the genuine drive history by subtracting out this baseline, leaving an excess that is strictly controlled by the accumulated imaginary-energy action and persists over the entire post-ramp time window. A connected longitudinal correlation mirrors this physics. Its slow-ramp growth tracks the corresponding doubled action. Unstable sectors instead continue amplifying post-ramp if the drive halts inside the broken-spectrum region. Exceptional points yield distinct physics. The finite-time propagator and subsystem correlation matrix remain entirely regular near an exceptional endpoint, even as the quasiparticle gap exhibits its characteristic square-root closing. This finite-time regularity reflects the analyticity of the matrix evolution in the endpoint parameter; a diagonalizable endpoint is strictly not required. A diverging long-time crossover eventually reveals the exceptional scale. We halt the drive exactly at the exceptional point to find that the correlation projector and the connected longitudinal correlation share an identical ballisti front. The subsystem saturation length establishes a distinct but comparable spatial scale. Memory and exceptional-endpoint scalings show no divergence across the tested negative-imbalance range. Memory scaling is fixed by the drive and remains insensitive to the specific choice of real-spectrum final endpoint.

cond-mat.stat-mech↗
arXiv2026

Multidimensional dynamical centrality from Green functions in complex networks

Conventional centrality measures provide compact descriptions of node importance, but they emphasize specific structural relations and do not directly resolve the temporal and spectral organization of dynamical perturbation responses. Building on the Green function of a linearized networked system, we develop a multidimensional framework for dynamical node characterization. From the same response function, we extract three complementary indicators---Influence, Efficiency, and Distortion---that quantify cumulative response strength, temporal rate of response, and spectral concentration, respectively, together with a contribution matrix that resolves these quantities into source--target pathways. As a numerical demonstration, we apply the framework to weighted Kuramoto--Sakaguchi dynamics on heterogeneous Barabási--Albert networks. The three indicators distinguish implanted dynamical node classes through complementary dimensions of the perturbation response, while remaining strongly coupled to conventional topological centralities. These results demonstrate how a common dynamical response can be decomposed into distinct, physically interpretable characteristics rather than represented by a single aggregate descriptor. We finally discuss the scope and limitations of the linear-response assumption and extensions to time-dependent and nonlinear regimes.

cond-mat.stat-mech↗