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Phase Transitions

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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...

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Optogenetic Phase Transition of TDP-43 in Spinal Motor Neurons of Zebrafish Larvae

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Absorbing phase transitions in deterministic fixed-energy sandpile models.

¹Department of Physics, The Catholic University of Korea, Bucheon 14662, Republic of Korea.

Physical Review. E

|May 20, 2018

Summary

We explored the difference between Abelian sandpile models (ASM) and deterministic fixed-energy sandpile models (DFES). DFES exhibit multiple absorbing phase transitions (APT) with universal critical phenomena, distinct from ASM steady states.

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Area of Science:

Complex Systems
Statistical Physics
Dynamical Systems

Background:

Abelian sandpile models (ASM) exhibit steady-state behavior.
Deterministic fixed-energy sandpile models (DFES) present unique transition dynamics.
A noted difference exists between ASM steady states and DFES transition points.

Purpose of the Study:

Investigate the origin of the discrepancy between ASM steady state density and DFES transition points.
Analyze the absorbing phase transition (APT) in DFES.
Clarify the relationship between DFES dynamics and percolation theory.

Main Methods:

Theoretical analysis of DFES configuration space.
Numerical simulations of the 2D DFES with the Bak-Tang-Wiesenfeld (BTW-FES) toppling rule.
Examination of the impact of infinite-size and infinite-time limits.

Main Results:

DFES configuration space divides into classes leading to absorbing states or not.
Multiple transition points exist in DFES, dependent on initial configurations.
Critical phenomena at DFES transition points are universal.
The microscopic absorbing phase transition in BTW-FES relates to isotropic percolation, not self-organized criticality.

Conclusions:

The difference between ASM and DFES arises from their distinct dynamical behaviors and state spaces.
DFES can exhibit multiple absorbing phase transitions.
The transition dynamics of DFES are linked to percolation processes.
Recurrent ASM configurations do not yield nontrivial APT in DFES.