scholarly journals Determination of the critical exponents for the isotropic-nematic phase transition in a system of long rods on two-dimensional lattices: Universality of the transition

2008 ◽  
Vol 82 (5) ◽  
pp. 50007 ◽  
Author(s):  
D. A. Matoz-Fernandez ◽  
D. H. Linares ◽  
A. J. Ramirez-Pastor
Keyword(s):  
Phase Transition ◽  
Critical Exponents ◽  
Nematic Phase ◽  
Two Dimensional

scholarly journals Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents

2009 ◽  
Vol 2009 ◽  
pp. 1-22 ◽  
Author(s):  
Edson D. Leonel
Keyword(s):  
Phase Transition ◽  
Critical Exponents ◽  
Scaling Laws ◽  
Scaling Function ◽  
Initial Conditions ◽  
Invariant Tori ◽  
Dynamical Variable ◽  
Two Dimensional ◽  
Control Parameters ◽  
Average Value

A phase transition from integrability to nonintegrability in two-dimensional Hamiltonian mappings is described and characterized in terms of scaling arguments. The mappings considered produce a mixed structure in the phase space in the sense that, depending on the combination of the control parameters and initial conditions, KAM islands which are surrounded by chaotic seas that are limited by invariant tori are observed. Some dynamical properties for the largest component of the chaotic sea are obtained and described in terms of the control parameters. The average value and the deviation of the average value for chaotic components of a dynamical variable are described in terms of scaling laws, therefore critical exponents characterizing a scaling function that describes a phase transition are obtained and then classes of universality are characterized. The three models considered are: The Fermi-Ulam accelerator model, a periodically corrugate waveguide, and variant of the standard nontwist map.

Critical exponents at a reentrant isotropic–calamitic nematic phase transition

2004 ◽  
Vol 333 (1-2) ◽  
pp. 120-123 ◽  
Author(s):  
M. Simões ◽  
A. de Campos ◽  
P.A. Santoro ◽  
A.J. Palangana
Keyword(s):  
Phase Transition ◽  
Critical Exponents ◽  
Nematic Phase

CRITICAL SPIN-1 VERTEX MODELS AND O(n) MODELS

1990 ◽  
Vol 04 (05) ◽  
pp. 929-942 ◽  
Author(s):  
Bernard NIENHUIS
Keyword(s):  
Critical Points ◽  
Critical Exponents ◽  
Square Lattice ◽  
Two Dimensional ◽  
Planar Lattice ◽  
Vertex Models ◽  
Critical Manifold ◽  
Multicritical Points ◽  
Straightforward Generalization

A method is presented by which critical and multicritical points of spin-1 (three-state) vertex models and classical O(n) models on two-dimensional lattices are determined. It is a straightforward generalization of the ideas that earlier led to the determination of critical points and critical exponents of a honeycomb O(n) model. On the square lattice the methods leads to tricritical as well as critical loci. For n=2 a larger critical manifold is found than for other values of n. At the critical and multicritical points thus produced the models turn out to be soluble. The method is applicable to O(n) models and spin-1 vertex models on any planar lattice.

ON THE DETERMINATION OF CRITICAL POINT IN HIGHER-ORDER VARIATIONAL CUMULANT EXPANSION

1996 ◽  
Vol 10 (12) ◽  
pp. 531-536 ◽  
Author(s):  
X.F. OU ◽  
J.T. OU ◽  
D.L. LIN
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Phase Transitions ◽  
Ising Model ◽  
Critical Point ◽  
Spin System ◽  
Order Approximation ◽  
Two Dimensional ◽  
Cumulant Expansion

To the lowest order approximation, the method of variational cumulant expansion has been successful in the determination of the critical point of a spin system on the Ising model. In the second order calculation, unphysical phase transition arises. In this letter, we first analyze the origin of unphysical phase transitions in high-order variational cumulant expansion calculations. We then explain the basis on which a conjecture is proposed that to any order m of the variational cumulant expansion, the critical point is given by the bifurcation point of the free energy. The theory is finally verified numerically for the two-dimensional case.

Critical Magnetism of the CMR Ruddlesden-Popper Manganite La1.2Sr1.8Mn2O7

2001 ◽  
Vol 690 ◽  
Author(s):  
Matias Velázquez ◽  
Alexandre Revcolevschi ◽  
Jean-Pierre Renard ◽  
Claire Dupasa
Keyword(s):  
Magnetic Properties ◽  
Curie Temperature ◽  
Critical Exponents ◽  
Magnetic System ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Narrow Temperature Range ◽  
Critical Fluctuations ◽  
Ferromagnetic Ordering

ABSTRACTWe present a thermodynamic study of the critical magnetic properties of La1.2Sr1.8Mn2O7, including the determination of the fundamental characteristics of a magnetic system: anisotropy, critical exponents and crossovers in the vicinity of the Curie temperature, TC∼108K. It appears that two-dimensional correlations above TC do not spread very fast, and that thus the critical fluctuations regime occurs in a moderately narrow temperature range, assessing the three- dimensional nature of the ferromagnetic ordering.

scholarly journals Spherical model and quantum phase transitions

2021 ◽  
Vol 2094 (2) ◽  
pp. 022027
Author(s):  
V N Udodov
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Critical Temperature ◽  
Critical Exponents ◽  
Quantum Phase Transitions ◽  
Dimensional Space ◽  
Spherical Model ◽  
Quantum Phase ◽  
Two Dimensional ◽  
Epsilon Expansion

Abstract The spherical Berlin-Katz model is considered in the framework of the epsilon expansion in one-dimensional and two-dimensional space. For the two-dimensional and threedimensional cases in this model, an exact solution was previously obtained in the presence of a field, and for the two-dimensional case the critical temperature is zero, that is, a “quantum” phase transition is observed. On the other hand, the epsilon expansion of critical exponents with an arbitrary number of order parameter components is known. This approach is consistent with the scaling paradigm. Some critical exponents are found for the spherical model in one-and twodimensional space in accordance with the generalized scaling paradigm and the ideas of quantum phase transitions. A new formula is proposed for the critical heat capacity exponent, which depends on the dynamic index z, at a critical temperature equal to zero. An expression is proposed for the order of phase transition with a change in temperature (developing the approach of R. Baxter), which also depends on the z index. An interpolation formula is presented for the effective dimension of space, which is valid for both a positive critical temperature and a critical temperature equal to zero. This formula is general. Transitions with a change in the field in a spherical model at absolute zero are also considered.

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