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.

A NEW SOLVABLE 3D MODEL OF STATISTICAL MECHANICS: THE FREE-FERMION SOLUTION

1996 ◽  
Vol 10 (04) ◽  
pp. 443-453 ◽  
Author(s):  
A.E. BOROVICK ◽  
S.I. KULINICH ◽  
V. Yu. POPKOV ◽  
Yu. M. STRZHEMECHNY
Keyword(s):  
Phase Diagram ◽  
Statistical Mechanics ◽  
Bethe Ansatz ◽  
3D Model ◽  
Nearest Neighbor ◽  
Baxter Equation ◽  
Free Fermion ◽  
Vertex Model ◽  
Free Fermions ◽  
Exactly Solvable

We obtain a new exactly solvable K-plane vertex model. This 3D model is one wih real Boltzmann weights and nearest neighbor interactions. The corresponding Yang-Baxter equation is proved. The Bethe ansatz has also been found, enabling us to completely investigate the phase diagram in the “free fermions” case.

scholarly journals Двумерные O(n)-модели с дефектами типа "случайная локальная анизотропия"

2020 ◽  
Vol 62 (4) ◽  
pp. 610
Author(s):  
А.А. Берзин ◽  
А.И. Морозов ◽  
А.С. Сигов
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Order Parameter ◽  
Easy Axis ◽  
Critical Value ◽  
Smooth Transition ◽  
Two Dimensional ◽  
Continuous Symmetry ◽  
Local Anisotropy ◽  
Ordered State

The phase diagram of two-dimensional systems with continuous symmetry of the vector order parameter containing defects of the “random local anisotropy” type is investigated. In the case of a weakly anisotropic distribution of the easy anisotropy axes in the space of the order parameter, with decreasing temperature, a smooth transition takes place from the paramagnetic phase with dynamic fluctuations of the order parameter to the Imri-Ma phase with its static fluctuations. In the case when the anisotropic distribution of the easy axes induces a global anisotropy of the “easy axis” type that exceeds a critical value, the system goes into the Ising class of universality, and a phase transition to the ordered state occurs in it at a finite temperature.

FERMIONIC STRINGS AND THE EXACT SOLUTION OF EDGE MODELS IN THREE DIMENSIONS

1991 ◽  
Vol 05 (14) ◽  
pp. 2401-2438 ◽  
Author(s):  
PETER ORLAND
Keyword(s):  
Phase Diagram ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Conformal Anomaly ◽  
Two Dimensional ◽  
Vertex Model ◽  
Statistical System ◽  
Roughening Transition ◽  
Exactly Solvable ◽  
Domain Of Parameters

A three-dimensional statistical system, called here the six-edge model, is shown, for a particular domain of parameters, to be equivalent to a theory of Fermionic strings. This model has a local U(1) gauge invariance, similiar to the global invariance of the two-dimensional six-vertex model. Further restricting the parameters gives a system named here the five-edge model, which is exactly solvable. The conformal anomaly of the surfaces is calculated. The transfer matrix is diagonalized, and the free energy, phase diagram and correlation length are determined exactly. The surfaces of the model display a roughening transition similiar to that analyzed by Blöte, Hilhorst and Nienhuis.

scholarly journals On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

2021 ◽  
Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga
Keyword(s):  
Free Energy ◽  
Dimension Reduction ◽  
Three Dimensional ◽  
Energy Functional ◽  
The Other ◽  
Variational Model ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Kinematic Constraint ◽  
Free Energy Functional

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

COMPLEX BIFURCATION STRUCTURES IN THE HINDMARSH–ROSE NEURON MODEL

2007 ◽  
Vol 17 (09) ◽  
pp. 3071-3083 ◽  
Author(s):  
J. M. GONZÀLEZ-MIRANDA
Keyword(s):  
Phase Diagram ◽  
Bifurcation Diagram ◽  
Parameter Space ◽  
Neuron Model ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
Rapid Responses ◽  
Bifurcation Structures

The results of a study of the bifurcation diagram of the Hindmarsh–Rose neuron model in a two-dimensional parameter space are reported. This diagram shows the existence and extent of complex bifurcation structures that might be useful to understand the mechanisms used by the neurons to encode information and give rapid responses to stimulus. Moreover, the information contained in this phase diagram provides a background to develop our understanding of the dynamics of interacting neurons.

scholarly journals Universal behavior of the bosonic metallic ground state in a two-dimensional superconductor

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Zhuoyu Chen ◽  
Bai Yang Wang ◽  
Adrian G. Swartz ◽  
Hyeok Yoon ◽  
Yasuyuki Hikita ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Phase Diagram ◽  
Quantum Phase Transitions ◽  
Metallic State ◽  
Two Dimensional ◽  
Metallic Behavior ◽  
Universal Behavior ◽  
Hall Resistivity ◽  
Wide Range ◽  
Metal State

AbstractAnomalous metallic behavior, marked by a saturating finite resistivity much lower than the Drude estimate, has been observed in a wide range of two-dimensional superconductors. Utilizing the electrostatically gated LaAlO3/SrTiO3 interface as a versatile platform for superconductor-metal quantum phase transitions, we probe variations in the gate, magnetic field, and temperature to construct a phase diagram crossing from superconductor, anomalous metal, vortex liquid, to the Drude metal state, combining longitudinal and Hall resistivity measurements. We find that the anomalous metal phases induced by gating and magnetic field, although differing in symmetry, are connected in the phase diagram and exhibit similar magnetic field response approaching zero temperature. Namely, within a finite regime of the anomalous metal state, the longitudinal resistivity linearly depends on the field while the Hall resistivity diminishes, indicating an emergent particle-hole symmetry. The universal behavior highlights the uniqueness of the quantum bosonic metallic state, distinct from bosonic insulators and vortex liquids.

Low-density phase diagram of the two-dimensional Coulomb gas

1986 ◽  
Vol 33 (1) ◽  
pp. 499-509 ◽  
Author(s):  
J. M. Caillol ◽  
D. Levesque
Keyword(s):  
Phase Diagram ◽  
Coulomb Gas ◽  
Low Density ◽  
Two Dimensional
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