Critical behavior of a fully frustrated classicalXYmodel in two dimensions

1991 ◽  
Vol 44 (18) ◽  
pp. 10057-10065 ◽  
Author(s):  
Julio F. Fernández ◽  
Marcello Puma ◽  
Rafael F. Angulo
Keyword(s):  
Critical Behavior ◽  
Two Dimensions

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.

A critical behavior of the Lennard–Jones dimeric fluid in two-dimensions.

2011 ◽  
Vol 605 (13-14) ◽  
pp. 1219-1223 ◽  
Author(s):  
W. Rżysko ◽  
M. Borówko
Keyword(s):  
Critical Behavior ◽  
Two Dimensions ◽  
Lennard Jones

scholarly journals EFFECT OF FIELD DIRECTION AND FIELD INTENSITY ON DIRECTED SPIRAL PERCOLATION

2006 ◽  
Vol 17 (09) ◽  
pp. 1285-1302 ◽  
Author(s):  
SANTANU SINHA ◽  
S. B. SANTRA
Keyword(s):  
Phase Diagram ◽  
Critical Behavior ◽  
Disordered Systems ◽  
Universality Class ◽  
Two Dimensions ◽  
Percolation Model ◽  
Field Direction ◽  
Critical Properties ◽  
External Bias ◽  
Directional Field

Directed spiral percolation (DSP) is a new percolation model with crossed external bias fields. Since percolation is a model of disorder, the effect of external bias fields on the properties of disordered systems can be studied numerically using DSP. In DSP, the bias fields are an in-plane directional field (E) and a field of rotational nature (B) applied perpendicular to the plane of the lattice. The critical properties of DSP clusters are studied here varying the direction of E field and intensities of both E and B fields in two-dimensions. The system shows interesting and unusual critical behavior at the percolation threshold. Not only the DSP model is found to belong in a new universality class compared to that of other percolation models but also the universality class remains invariant under the variation of E field direction. Varying the intensities of the E and B fields, a crossover from DSP to other percolation models has been studied. A phase diagram of the percolation models is obtained as a function of intensities of the bias fields E and B.

Wetting of a Disordered Substrate: Exact Critical Behavior in Two Dimensions

1986 ◽  
Vol 57 (17) ◽  
pp. 2184-2187 ◽  
Author(s):  
G. Forgacs ◽  
J. M. Luck ◽  
Th. M. Nieuwenhuizen ◽  
H. Orland
Keyword(s):  
Critical Behavior ◽  
Two Dimensions

scholarly journals Critical behavior of weakly disordered anisotropic systems in two dimensions

1996 ◽  
Vol 54 (5) ◽  
pp. 3442-3453 ◽  
Author(s):  
Giancarlo Jug ◽  
Boris N. Shalaev
Keyword(s):  
Critical Behavior ◽  
Two Dimensions ◽  
Anisotropic Systems

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.

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