Critical point fluctuations: Finite size and global charge conservation effects

Abstract

We investigate simultaneous effects of finite system size and global charge conservation on thermal fluctuations in the vicinity of a critical point. For that we consider a finite interacting system which exchanges particles with a finite reservoir (thermostat), comprising a statistical ensemble that is distinct from the common canonical and grand canonical ensembles. As a particular example the van der Waals model is used. The global charge conservation effects strongly influence the cumulants of particle number distribution when the system size is comparable to that of the reservoir. If the system size is large enough to capture all the physics associated with the interactions, the global charge conservation effects can be accurately described and corrected for analytically, within a recently developed subensemble acceptance method. The finite size effects start to play a significant role when the correlation length grows large due to proximity of the critical point or when the system is small enough to be comparable to an eigenvolume of an individual particle. We discuss our results in the context of fluctuation measurements in heavy-ion collisions.

arXiv comment11 pages, 5 figures

References in corpus (45)

• Signatures of the Tricritical Point in QCD
• Event-by-Event Fluctuations in Heavy Ion Collisions and the QCD Critical Point
• Non-Gaussian fluctuations near the QCD critical point
• On the sign of kurtosis near the QCD critical point
• Fluctuations of conserved charges at finite temperature from lattice QCD
• Fluctuations and Correlations of net baryon number, electric charge, and strangeness: A comparison of lattice QCD results with the hadron resonance gas model
• Universality, the QCD critical/tricritical point and the quark number susceptibility
• Three-loop HTLpt thermodynamics at finite temperature and chemical potential
• Freeze-out conditions from net-proton and net-charge fluctuations at RHIC
• Hydro+: hydrodynamics with parametric slowing down and fluctuations near the critical point
• van der Waals Interactions in Hadron Resonance Gas: From Nuclear Matter to Lattice QCD
• Skewness, kurtosis and the 5th and 6th order cumulants of net baryon-number distributions from lattice QCD confront high-statistics STAR data
• Critical point in the phase diagram of primordial quark-gluon matter from black hole physics
• Using Higher Moments of Fluctuations and their Ratios in the Search for the QCD Critical Point
• Relation between baryon number fluctuations and experimentally observed proton number fluctuations in relativistic heavy ion collisions
• Real time evolution of non-Gaussian cumulants in the QCD critical regime
• Acceptance corrections to net baryon and net charge cumulants
• Revealing baryon number fluctuations from proton number fluctuations in relativistic heavy ion collisions
• Strongly Intensive Quantities
• Bridging the gap between event-by-event fluctuation measurements and theory predictions in relativistic nuclear collisions
• Particle Number Fluctuations in Canonical Ensemble
• Diffusive dynamics of critical fluctuations near the QCD critical point
• Baryon number fluctuations in the QCD phase diagram from Dyson-Schwinger equations
• Equation of state for hot QCD and compact stars from a mean field approach
• Van der Waals Equation of State with Fermi Statistics for Nuclear Matter
• Baryon number fluctuations at finite temperature and density
• Cluster Expansion Model for QCD Baryon Number Fluctuations: No Phase Transition at ${\mu }_B/T<\pi$
• Higher-order baryon number susceptibilities: interplay between the chiral and the nuclear liquid-gas transitions
• Fluctuations and correlations of conserved charges in an excluded volume hadron resonance gas model
• Transits of the QCD Critical Point
• Phase transition of a finite quark-gluon plasma
• Particle Number Fluctuations for van der Waals Equation of State
• Chemical freeze-out conditions and fluctuations of conserved charges in heavy-ion collisions within quantum van der Waals model
• Efficient formulas for efficiency correction of cumulants
• Large proton cumulants from the superposition of ordinary multiplicity distributions
• Binomial acceptance corrections for particle number distributions in high-energy reactions
• Non-Gaussian particle number fluctuations in vicinity of the critical point for van der Waals equation of state
• Quantum van der Waals and Walecka models of nuclear matter
• Traces of the nuclear liquid-gas phase transition in the analytic properties of hot QCD
• Effect of finite particle number sampling on baryon number fluctuations
• Monte Carlo approach to the excluded-volume hadron resonance gas in grand canonical and canonical ensembles
• Strongly Intensive Cumulants: Fluctuation Measures for Systems With Incompletely Constrained Volumes
• Dynamics of critical fluctuations: Theory -- phenomenology -- heavy-ion collisions
• The balance of attractive and repulsive hadronic interactions: the influence of hadronic spectrum and excluded volume effects on lattice thermodynamics and consequences on experiments
• Effects of fluctuations and color-neutrality in a finite volume

Cited by in corpus (17)

• Connecting fluctuation measurements in heavy-ion collisions with the grand-canonical susceptibilities
• Particlization of an interacting hadron resonance gas with global conservation laws for event-by-event fluctuations in heavy-ion collisions
• Quartic cumulant of baryon number in the presence of QCD critical point
• Cumulants of multiple conserved charges and global conservation laws
• Phase transition amplification of proton number fluctuations in nuclear collisions from a transport model approach
• Higher order conserved charge fluctuations inside the mixed phase
• Molecular dynamics analysis of particle number fluctuations in the mixed phase of a first-order phase transition
• Coordinate versus momentum cuts and effects of collective flow on critical fluctuations
• Effects of centrality fluctuation and deuteron formation on proton number cumulant in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 3 GeV from JAM model
• Effect of finite volume on thermodynamics of quark-hadron matter
• Possible origin of HADES data on proton number fluctuations in Au+Au collisions
• Non-equilibrium cumulants within model A from crossover to first-order phase transition side
• Cumulants from short-range correlations and baryon number conservation - next-to-leading order
• Fluctuations in heavy ion collisions and global conservation effects
• Intermittency of charged particles in the hybrid UrQMD+CMC model at energies available at the BNL Relativistic Heavy Ion Collider
• Critical point particle number fluctuations from molecular dynamics
• Particle-number fluctuations near the critical point of nuclear matter