Identifying transitions in finite systems by means of partition function zeros and microcanonical inflection-point analysis: A comparison for elastic flexible polymers

Abstract

For the estimation of transition points of finite elastic, flexible polymers with chain lengths from $13$ to $309$ monomers, we compare systematically transition temperatures obtained by the Fisher partition function zeros approach with recent results from microcanonical inflection-point analysis. These methods rely on accurate numerical estimates of the density of states, which have been obtained by advanced multicanonical Monte Carlo sampling techniques. Both the Fisher zeros method and microcanonical inflection-point analysis yield very similar results and enable the unique identification of transition points in finite systems, which is typically impossible in the conventional canonical analysis of thermodynamic quantities.

11 pages and 5 figures

References in corpus (19)

• Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms
• An efficient, multiple range random walk algorithm to calculate the density of states
• Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions
• Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
• Microcanonical Analyses of Peptide Aggregation Processes
• Microcanonical entropy inflection points: Key to systematic understanding of transitions in finite systems
• Freezing and Collapse of Flexible Polymers on Regular Lattices in Three Dimensions
• Multicanonical Simulations Step by Step
• Structural transitions in the 309-atom magic number Lennard-Jones cluster
• Partition Function Zeros and Finite Size Scaling of Helix-Coil Transitions in a Polypeptide
• Elastic Lennard-Jones Polymers Meet Clusters -- Differences and Similarities
• Surface effects in the crystallization process of elastic flexible polymers
• Thermodynamics of Peptide Aggregation Processes. An Analysis from Perspectives of Three Statistical Ensembles
• Systematic Microcanonical Analyses of Polymer Adsorption Transitions
• Advanced multicanonical Monte Carlo methods for efficient simulations of nucleation processes of polymers
• Statistical Mechanics of Aggregation and Crystallization for Semiflexible Polymers
• Phase transition strengths from the density of partition function zeroes
• Density of Partition Function Zeroes and Phase Transition Strength
• Stripe-tetragonal phase transition in the 2D Ising model with dipole interactions: Partition-function zeros approach

Cited by in corpus (11)

• Energy Probability Distribution Zeros: A Route to Study Phase Transitions
• The fully frustrated XY model revisited: A new universality class
• Using zeros of the canonical partition function map to detect signatures of a Berezinskii-Kosterlitz-Thouless transition
• Partition function zeros of the p-state clock model in the complex temperature plane
• Autocorrelation study of the Θ transition for a coarse-grained polymer model
• Microcanonical thermostatistics analysis without histograms: cumulative distribution and Bayesian approaches
• Time correlation functions and Fisher zeros for q-deformed Bose gas
• Microcanonical analysis of a nonequilibrium phase transition
• Wang-Landau simulations with non-flat distributions
• Finding the Dominant Zero of the Energy Probability Distribution
• Determination of melting temperature of hexagonal ice using Lee-Yang phase transition theory