Critical behavior at the ferromagnetic phase transition of (Fe1−xCrx)85B15metallic glasses close to the critical concentration of ferromagnetic long-range order

1990 ◽  
Vol 41 (1) ◽  
pp. 740-748 ◽  
Author(s):  
U. Güntzel ◽  
K. Westerholt
Keyword(s):  
Phase Transition ◽  
Long Range ◽  
Critical Behavior ◽  
Critical Concentration ◽  
Range Order ◽  
Ferromagnetic Phase ◽  
Long Range Order ◽  
Ferromagnetic Phase Transition

scholarly journals TOWARD A PROOF OF LONG RANGE ORDER IN 4D SU(N) LATTICE GAUGE THEORY

2013 ◽  
Vol 28 (19) ◽  
pp. 1350087 ◽  
Author(s):  
MICHAEL GRADY
Keyword(s):  
Phase Transition ◽  
Gauge Theory ◽  
Long Range ◽  
Lattice Gauge Theory ◽  
Coulomb Gauge ◽  
Range Order ◽  
Spontaneous Breaking ◽  
Ferromagnetic Phase ◽  
Long Range Order ◽  
Lattice Gauge

An extended version of four-dimensional (4D) SU(2) lattice gauge theory is considered in which different inverse coupling parameters are used, [Formula: see text] for plaquettes which are purely space-like, and βV for those which involve the Euclidean time-like direction. It is shown that when βH = ∞ the partition function becomes, in the Coulomb gauge, exactly that of a set of non-interacting three-dimensional (3D) O(4) classical Heisenberg models. Long range order (LRO) at low temperatures (weak coupling) has been rigorously proven for this model. It is shown that the correlation function demonstrating spontaneous magnetization in the ferromagnetic phase is a continuous function of gH at gH = 0 and therefore, that the spontaneously broken phase enters the (βH, βV) phase plane (no step discontinuity at the edge). Once the phase transition line has entered, it can only exit at another identified edge, which requires the SU(2) gauge theory within also to have a phase transition at finite β. A phase exhibiting spontaneous breaking of the remnant symmetry left after Coulomb gauge fixing, the relevant symmetry here, is non-confining. Easy extension to the SU (N) case implies that the continuum limit of zero-temperature 4D SU (N) lattice gauge theories is not confining, in other words, gluons by themselves do not produce a confinement.

LONG RANGE ORDER IN THE BLUME-EMERY-GRIFFITHS MODEL

1991 ◽  
Vol 05 (23) ◽  
pp. 1583-1590
Author(s):  
M. CORGINI
Keyword(s):  
Phase Transition ◽  
Long Range ◽  
Order Phase Transition ◽  
Range Order ◽  
Long Range Order ◽  
First Order ◽  
First Order Phase Transition ◽  
Infrared Bounds ◽  
First Order Phase

Using the Infrared Bounds method it ws demonstrated that a first order phase transition takes place in the m-dimensional (m≥3) Blume-Emery-Griffiths model.

Study of a model for the main phase transition of lipid bilayers using the Kikuchi cluster method

1984 ◽  
Vol 62 (9) ◽  
pp. 935-942 ◽  
Author(s):  
Alzira M. Stein-Barana ◽  
G. G. Cabrera ◽  
M. J. Zuckermann
Keyword(s):  
Phase Transition ◽  
Lipid Bilayers ◽  
Long Range ◽  
Effective Field ◽  
Order Parameters ◽  
Range Order ◽  
Cluster Method ◽  
Variation Method ◽  
Long Range Order ◽  
Approximate Counting

The statistical mechanics of Doniach's two-state lattice model for the main gel – liquid crystal phase transition of phospholipid bilayers is treated in a similar manner to order–disorder transformations in binary alloys and magnetic systems, using the cluster variation method developed by Kikuchi. Indeed, the analogy holds better for the latter system, since the entropy difference between the two states gives rise to an effective temperature-dependent field. This effective field vanishes at the first-order phase transition, whose latent heat is associated with the discontinuity in the order parameter.We use Kikuchi's approximation with the inclusion of triangle bond correlations, and pair and site probabilities in the expression for free energy. We assume that the lipid chains only interact through nearest neighbour pair potentials and that triangle correlations are important for approximate counting of allowed states. Two long-range order parameters and a short-range order parameter are introduced in the formulation of the theory. Both long-range order parameters are discontinuous at the transition temperature. Numerical results for the physical quantities are presented and discussed with respect to earlier work.

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