Suppression of the Order Parameter Correlation Length by Inhomogeneous Strains

2000 ◽  
Vol 85 (13) ◽  
pp. 2765-2768 ◽  
Author(s):  
A. Tröster ◽  
W. Schranz ◽  
G. Krexner ◽  
A. V. Kityk ◽  
Z. Lodziana
Keyword(s):  
Correlation Length ◽  
Order Parameter ◽  
Parameter Correlation

SIX-VERTEX MODELS AS FERMI GASES

1991 ◽  
Vol 05 (14) ◽  
pp. 2385-2400
Author(s):  
PETER ORLAND
Keyword(s):  
Phase Diagram ◽  
Free Energy ◽  
Order Parameter ◽  
Fermi Gases ◽  
Two Dimensional ◽  
Vertex Model ◽  
Energy Correlation ◽  
Free Fermions ◽  
Parameter Correlation ◽  
Simple Physical Interpretation

The two-dimensional six-vertex model with a particular choice of external field is known to be equivalent to a theory of free Fermions. Two conditions are made on the six-vertex weights. A simple physical interpretation of the ordered and disordered phases is found. The Fermi sea is filled and the free energy, correlation length, order parameter, correlation functions and phase diagram are determined.

scholarly journals Shear bands as manifestation of a criticality in yielding amorphous solids

2017 ◽  
Vol 114 (22) ◽  
pp. 5577-5582 ◽  
Author(s):  
Giorgio Parisi ◽  
Itamar Procaccia ◽  
Corrado Rainone ◽  
Murari Singh
Keyword(s):  
Correlation Length ◽  
Order Parameter ◽  
Shear Bands ◽  
Amorphous Solids ◽  
Applied Strain ◽  
Mean Stress ◽  
Controlled Experiments ◽  
Generic Theory ◽  
Thermodynamic Phase ◽  
Huge Variety

Amorphous solids increase their stress as a function of an applied strain until a mechanical yield point whereupon the stress cannot increase anymore, afterward exhibiting a steady state with a constant mean stress. In stress-controlled experiments, the system simply breaks when pushed beyond this mean stress. The ubiquity of this phenomenon over a huge variety of amorphous solids calls for a generic theory that is free of microscopic details. Here, we offer such a theory: The mechanical yield is a thermodynamic phase transition, where yield occurs as a spinodal phenomenon. At the spinodal point, there exists a divergent correlation length that is associated with the system-spanning instabilities (also known as shear bands), which are typical to the mechanical yield. The theory, the order parameter used, and the correlation functions that exhibit the divergent correlation length are universal in nature and can be applied to any amorphous solids that undergo mechanical yield.

scholarly journals Correlations in Space and Time for a Soft-mode Phase-transforming System

1987 ◽  
Vol 40 (5) ◽  
pp. 619 ◽  
Author(s):  
SL Mair
Keyword(s):  
Correlation Function ◽  
Frequency Spectrum ◽  
Order Parameter ◽  
Central Peak ◽  
Square Lattice ◽  
Order Component ◽  
Low Frequencies ◽  
Potential Wells ◽  
Parameter Correlation ◽  
Dynamical Order

Using molecular dynamics (MD) for a system of.nonlinear (quadruple-quadratic) oscillators on a nearest-neighbour square lattice, the pair-displacement correlations. and the frequency spectrum for the dynamical order-parameter correlation function are obtained as a function of temperature. For temperatures T near Tc' the pair-displacement correlation function (with the long-range order component subtracted out) was found to vary with particle separation r as r- 1/2 exp { - A( T) rj, at least out to the tenth neighbour in the 40x40 particle lattice. This is consistent with predictions for the two-dimensional Ising model for T above, but not below, Tc. The frequency spectrum for the dynamical order-parameter correlation function shows the softening of the damped phonon-like modes as T approaches Tc and the formation of a central peak at Tc' consistent with the presence of soliton-like excitations. For small I T - Tc I an additional broad peak appears at low frequencies. This is interpreted as an additional phonon-like peak, the two quasi-phonon processes being associated with vibration across the potential barrier and vibration in one or other of the two potential wells respectively. Although the squared frequency wi of the soft quasi-phonon is approximately linear with I T - Tc lover a range of temperatures, as T increases the wi curve eventually flattens out.

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