Locating fixed points in the phase plane
arXiv:1905.11388 · doi:10.1103/PhysRevE.100.052146
Abstract
The critical point is a fixed point in finite-size scaling. To quantify the behaviour of such a fixed point, we define, at a given temperature and scaling exponent ratio, the width of scaled observables for different sizes. The minimum of the width reveals the position of fixed point, its corresponding phase transition temperature, and scaling exponent ratio. The value of this ratio tells the nature of fixed point, which can be a critical point, a point of the first order phase transition line, or a point of the crossover region. To demonstrate the effectiveness of this method, we apply it to three typical samples produced by the 3D three-state Potts model. Results show the method to be more precise and effective than conventional methods. Finally, we discuss a possible application at the beam energy scan program of relativistic heavy-Ion collision.
arXiv commentv3: final version. v2: references update. 7 pages, 4 figures. arXiv admin note: text overlap with arXiv:1805.04311
References in corpus (32)
- The order of the quantum chromodynamics transition predicted by the standard model of particle physics
- Non-Gaussian fluctuations near the QCD critical point
- Comparison of Chemical Freeze-Out Criteria in Heavy-Ion Collisions
- Recent advances in percolation theory and its applications
- Slowing Out of Equilibrium Near the QCD Critical Point
- Ising Universality in Three Dimensions: A Monte Carlo Study
- QCD at finite temperature and chemical potential from Dyson-Schwinger equations
- Scale for the Phase Diagram of Quantum Chromodynamics
- Baryon Number, Strangeness and Electric Charge Fluctuations in QCD at High Temperature
- The Time-Delay Signature of Quark-Gluon-Plasma Formation in Relativistic Nuclear Collisions
- Bose-Einstein Correlations for Three-Dimensionally Expanding, Cylindrically Symmetric, Finite Systems
- Using Higher Moments of Fluctuations and their Ratios in the Search for the QCD Critical Point
- The liquid to vapor phase transition in excited nuclei
- A new cross term in the two-particle Hanbury-Brown-Twiss correlation function
- Three-Dimensional 3-State Potts Model Revisited With New Techniques
- Observation of the critical end point in the phase diagram for hot and dense nuclear matter
- Ising transition driven by frustration in a 2D classical model with SU(2) symmetry
- Chiral transition in a finite system and possible use of finite size scaling in relativistic heavy ion collisions
- On the Phase Structure of QCD in a Finite Volume
- Equilibrium Statistical-Thermal Models in High-Energy Physics
- The three-dimensional, three-state Potts Model in an External Field
- Cumulants and Correlation Functions vs the QCD phase diagram
- Event-by-Event Analysis of Proton-Induced Nuclear Multifragmentation: Determination of Phase Transition Universality-Class in System with Extreme Finite-Size Constraints
- The scaling functions of the free energy density and its derivatives for the 3d O(4) model
- The Effect of Fluctuations on the QCD Critical Point in a Finite Volume
- Hadronization and Hadronic Freeze-Out in Relativistic Nuclear Collisions
- Monte Carlo study of the Villain version of the fully frustrated XY model
- Finite-size scaling as a tool in the search for the QCD critical point in heavy ion data
- Locating the QCD critical endpoint through finite-size scaling
- Indications for a critical point in the phase diagram for hot and dense nuclear matter
- Finite-Size Scaling of Non-Gaussian Fluctuations Near the QCD Critical Point
- Generalized susceptibilities along the phase boundary of the three-dimensional, three-state Potts model