On the two-dimensional Coulomb gas

1987 ◽  
Vol 49 (1-2) ◽  
pp. 33-56 ◽  
Author(s):  
Fran�oise Cornu ◽  
Bernard Jancovici
Keyword(s):  
Coulomb Gas ◽  
Two Dimensional

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

scholarly journals Variance of Voltages in a Lattice Coulomb Gas

2021 ◽  
Vol 186 (1) ◽  
Author(s):  
Diana Conache ◽  
Markus Heydenreich ◽  
Franz Merkl ◽  
Silke W. W. Rolles
Keyword(s):  
High Temperature ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Temperature Regime ◽  
Gaussian Model ◽  
Coulomb Gas ◽  
Two Dimensional ◽  
Discrete Gaussian Model ◽  
Dimensional Lattice ◽  
The Difference

AbstractWe study the behavior of the variance of the difference of energies for putting an additional electric unit charge at two different locations in the two-dimensional lattice Coulomb gas in the high-temperature regime. For this, we exploit the duality between this model and a discrete Gaussian model. Our estimates follow from a spontaneous symmetry breaking in the latter model.

First-order transition in the dense two-dimensional classical Coulomb gas

1993 ◽  
Vol 48 (16) ◽  
pp. 12304-12307 ◽  
Author(s):  
Guang-Ming Zhang ◽  
Hong Chen ◽  
Xiang Wu
Keyword(s):  
Coulomb Gas ◽  
Order Transition ◽  
Two Dimensional ◽  
First Order ◽  
First Order Transition ◽  
Classical Coulomb Gas

Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition

2017 ◽  
Vol 31 (06) ◽  
pp. 1730001 ◽  
Author(s):  
Jorge V. José
Keyword(s):  
Phase Structure ◽  
Vortex Pair ◽  
Spin Correlation ◽  
Coulomb Gas ◽  
Theoretical Physics ◽  
Xy Model ◽  
Two Dimensional ◽  
Theoretical Formulation ◽  
Abelian Gauge ◽  
Gauge Symmetries

In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii–Kosterlitz–Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson’s RG for lattice gauge theories. Although Migdal’s RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin–spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN’s results gave a theoretical formulation foundation and justification for BKT’s sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical [Formula: see text] temperature. The theoretical predictions were soon tested successfully against experimental results on superfluid helium films. The success of the BKT theory also gave one of the first quantitative proofs of the validity of the RG theory.

New critical behavior in the dense two-dimensional classical Coulomb gas

1990 ◽  
Vol 64 (13) ◽  
pp. 1483-1486 ◽  
Author(s):  
Jong-Rim Lee ◽  
S. Teitel
Keyword(s):  
Critical Behavior ◽  
Coulomb Gas ◽  
Two Dimensional ◽  
Classical Coulomb Gas
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