Critical behavior of commensurate-incommensurate phase transitions in two dimensions

1980 ◽  
Vol 22 (11) ◽  
pp. 5274-5277 ◽  
Author(s):  
H. J. Schulz
Keyword(s):  
Phase Transitions ◽  
Critical Behavior ◽  
Two Dimensions ◽  
Incommensurate Phase

Percolation

2017 ◽  
Author(s):  
Paul Charbonneau
Keyword(s):  
Phase Transitions ◽  
Water Vapor ◽  
Power Law ◽  
Critical Behavior ◽  
Scale Invariance ◽  
Granular Medium ◽  
Statistical Physics ◽  
Two Dimensions ◽  
Natural Systems ◽  
Fractal Clusters

This chapter explores a lattice-based system where complex structures can arise from pure randomness: percolation, typically described as the passage of liquid through a porous or granular medium. In its more abstract form, percolation is an exemplar of criticality, a concept in statistical physics related to phase transitions. A classic example of criticality is liquid water boiling into water vapor, or freezing into ice. The chapter first provides an overview of percolation in one and two dimensions before discussing the use of a tagging algorithm for identifying and sizing clusters. It then considers fractal clusters on a lattice at the percolation threshold, scale invariance of power-law behavior, and critical behavior of natural systems. The chapter includes exercises and further computational explorations, along with a suggested list of materials for further reading.

Critical behavior of a two-lattice model of antiferromagnetic phase transitions

1975 ◽  
Vol 12 (11) ◽  
pp. 5034-5042 ◽  
Author(s):  
V. A. Alessandrini ◽  
H. J. de Vega ◽  
F. Schaposnik
Keyword(s):  
Phase Transitions ◽  
Critical Behavior ◽  
Lattice Model ◽  
Antiferromagnetic Phase

Critical behavior of La0.7Ca0.3Mn1−xNixO3 manganites exhibiting the crossover of first- and second-order phase transitions

2014 ◽  
Vol 184 ◽  
pp. 40-46 ◽  
Author(s):  
The-Long Phan ◽  
Q.T. Tran ◽  
P.Q. Thanh ◽  
P.D.H. Yen ◽  
T.D. Thanh ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Critical Behavior ◽  
Second Order

scholarly journals A PERCOLATION MODEL OF DIAGENESIS

2002 ◽  
Vol 13 (03) ◽  
pp. 319-331 ◽  
Author(s):  
S. S. MANNA ◽  
T. DATTA ◽  
R. KARMAKAR ◽  
S. TARAFDAR
Keyword(s):  
Numerical Simulation ◽  
Critical Behavior ◽  
Sedimentary Rocks ◽  
Two Dimensions ◽  
Percolation Model ◽  
Type Model ◽  
Stable Configuration ◽  
Critical Percolation ◽  
Restructuring Process ◽  
Simulation Results

The restructuring process of diagenesis in the sedimentary rocks is studied using a percolation type model. The cementation and dissolution processes are modeled by the culling of occupied sites in rarefied and growth of vacant sites in dense environments. Starting from sub-critical states of ordinary percolation the system evolves under the diagenetic rules to critical percolation configurations. Our numerical simulation results in two dimensions indicate that the stable configuration has the same critical behavior as the ordinary percolation.

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