scholarly journals Becoming Large, Becoming Infinite: The Anatomy of Thermal Physics and Phase Transitions in Finite Systems

2021 ◽  
Vol 51 (5) ◽  
Author(s):  
David A. Lavis ◽  
Reimer Kühn ◽  
Roman Frigg
Keyword(s):  
Phase Transitions ◽  
Finite Size ◽  
Finite System ◽  
Finite Size Scaling ◽  
Thermal Physics ◽  
Finite Systems ◽  
Depth Analysis ◽  
Definition Of ◽  
Thermodynamics And Statistical Mechanics

AbstractThis paper presents an in-depth analysis of the anatomy of both thermodynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis, using the renormalization group and finite-size scaling, we give a definition of a large but finite system and argue that phase transitions are represented correctly, as incipient singularities in such systems. We describe the role of the thermodynamic limit. And we explore the implications of this picture of critical phenomena for the questions of reduction and emergence.

Phase Transitions, Critical Phenomena, and Finite-Size Scaling

2019 ◽  
pp. 111-176
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Critical Phenomena ◽  
Quantum Phase Transitions ◽  
Finite Size ◽  
System Size ◽  
Thermal Fluctuations ◽  
Finite Size Scaling ◽  
Size Scaling

Interacting many-particle systems may undergo phase transitions and exhibit critical phenomena in the limit of infinite system size, while the precursors of these phenomena are studied in the theory of finite-size scaling. After surveying the basic notions of phases, phase diagrams, and phase transitions, this chapter focuses on critical behaviour at a second-order phase transition. The Landau-Ginzburg theory and the concept of scaling prepare readers for an elementary introduction to the concepts of the renormalization group, followed by an introduction into the field of quantum phase transitions where quantum fluctuations take over the role of thermal fluctuations.

scholarly journals Macroscopic degeneracy and order in the 3D plaquette Ising model

2015 ◽  
Vol 29 (20) ◽  
pp. 1550109 ◽  
Author(s):  
Desmond A. Johnston ◽  
Marco Mueller ◽  
Wolfhard Janke
Keyword(s):  
Low Temperature ◽  
Magnetic Order ◽  
Finite Size ◽  
Temperature Phase ◽  
Finite Size Scaling ◽  
First Order ◽  
Magnetic Order Parameter ◽  
First Order Transition ◽  
Definition Of ◽  
Low Temperature Phase

The purely plaquette 3D Ising Hamiltonian with the spins living at the vertices of a cubic lattice displays several interesting features. The symmetries of the model lead to a macroscopic degeneracy of the low-temperature phase and prevent the definition of a standard magnetic order parameter. Consideration of the strongly anisotropic limit of the model suggests that a layered, “fuki-nuke” order still exists and we confirm this with multi-canonical simulations. The macroscopic degeneracy of the low-temperature phase also changes the finite-size scaling corrections at the first-order transition in the model and we see this must be taken into account when analyzing our measurements.

AN INVESTIGATION OF THE PHASE TRANSITIONS OF A FAMILY OF PROBABILISTIC AUTOMATA

2004 ◽  
Vol 07 (01) ◽  
pp. 93-123
Author(s):  
HEINZ MÜHLENBEIN ◽  
THOMAS AUS DER FÜNTEN
Keyword(s):  
Phase Transitions ◽  
Stationary Distribution ◽  
Classification Scheme ◽  
Mean Field ◽  
Finite Size ◽  
Order Parameters ◽  
Finite Size Scaling ◽  
Probabilistic Cellular Automata ◽  
Probabilistic Automata ◽  
Major Transitions

We investigate a family of totalistic probabilistic cellular automata (PCA) which depend on three parameters. For the uniform random neighborhood and for the symmetric 1D PCA the exact stationary distribution is computed for all finite n. This result is used to evaluate approximations (uni-variate and bi-variate marginals). It is proven that the uni-variate approximation (also called mean-field) is exact for the uniform random neighborhood PCA. The exact results and the approximations are used to investigate phase transitions. We compare the results of two order parameters, the uni-variate marginal and the normalized entropy. Sometimes different transitions are indicated by the Ehrenfest classification scheme. This result shows the limitations of using just one or two order parameters for detecting and classifying major transitions of the stationary distribution. Furthermore, finite size scaling is investigated. We show that extrapolations to n=∞ from numerical calculations of finite n can be misleading in difficult parameter regions. Here, exact analytical estimates are necessary.

scholarly journals Transmuted Finite-size Scaling at First-order Phase Transitions

2014 ◽  
Vol 57 ◽  
pp. 68-72 ◽  
Author(s):  
Marco Mueller ◽  
Wolfhard Janke ◽  
Desmond A. Johnston
Keyword(s):  
Phase Transitions ◽  
Finite Size ◽  
Finite Size Scaling ◽  
First Order ◽  
Size Scaling ◽  
First Order Phase

scholarly journals PERCOLATION AND FINITE SIZE SCALING IN SEVEN DIMENSIONS

2004 ◽  
Vol 15 (09) ◽  
pp. 1321-1325
Author(s):  
LOTFI ZEKRI
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Numerical Investigation ◽  
Critical Exponents ◽  
Finite Size ◽  
Critical Dimension ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Hypercubic Lattice

Numerical investigation of critical exponents on a hypercubic lattice with Ld random sites with L up to 33 and d up to 7 showed that above the critical dimension the phase transitions in Ising model and percolation are not alike.

DYNAMIC SCALING FOR FIRST-ORDER PHASE TRANSITIONS

2000 ◽  
Vol 11 (03) ◽  
pp. 553-559
Author(s):  
BANU EBRU ÖZOĞUZ ◽  
YIĞIT GÜNDÜÇ ◽  
MERAL AYDIN
Keyword(s):  
Phase Transitions ◽  
Finite Size ◽  
Two Dimensions ◽  
Dynamic Scaling ◽  
Finite Size Scaling ◽  
Potts Models ◽  
Time Dynamics ◽  
First Order ◽  
Short Time ◽  
First Order Phase

The critical behavior in short time dynamics for the q = 6 and 7 state Potts models in two-dimensions is investigated. It is shown that dynamic finite-size scaling exists for first-order phase transitions.

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