ar X iv : c on d - m at / 9 50 50 14 v 1 3 M ay 1 99 5 A Testbench for the Nested Dipole Hypothesis of Kosterlitz and Thouless
نویسندگان
چکیده
We consider the two-dimensional one-component plasma without a background and confined to a half plane near a metal wall. The particles are also subjected to an external potential acting perpendicular to the wall with an inverse power law Boltzmann factor. The model has a known solvable isotherm which exhibits a Kosterlitz-Thouless type transition from a conductive to an insulator phase as the power law is varied. This allows predictions of theoretical methods of analysing the Kosterlitz-Thouless transition to be compared with the exact solution. In particular we calculate the asymptotic density profile by resumming its low fugacity expansion near the zero-density critical coupling in the insulator phase, and solving a mean-field equation deduced from the first BGY equation. Agreement with the exact solution is obtained. As the former calculation makes essential use of the nested dipole hypothesis of Kosterlitz and Thouless, the validity of this hypothesis is explicitly verified.
منابع مشابه
ar X iv : c on d - m at / 9 50 10 33 v 1 9 J an 1 99 5 LAYERED XY - MODELS , ANYON SUPERCONDUCTORS , AND SPIN - LIQUIDS
The partition function of the double-layer XY model in the (dual) Villain form is computed exactly in the limit of weak coupling between layers. Both layers are found to be locked together through the Berezinskii-Kosterlitz-Thouless transition, while they become decoupled well inside the normal phase. These results are recovered in the general case of a finite number of such layers. When re-int...
متن کاملar X iv : c on d - m at / 9 50 50 15 v 1 3 M ay 1 99 5 CORRELATIONS IN TWO - COMPONENT LOG - GAS SYSTEMS
A systematic study of the properties of particle and charge correlation functions in the two-dimensional Coulomb gas confined to a one-dimensional domain is under-taken. Two versions of this system are considered: one in which the positive and negative charges are constrained to alternate in sign along the line, and the other where there is no charge ordering constraint. Both systems undergo a ...
متن کاملar X iv : c on d - m at / 9 30 50 01 v 1 3 M ay 1 99 3 One - dimensional asymmetrically coupled maps with defects
متن کامل
ar X iv : c on d - m at / 9 50 51 15 v 1 2 4 M ay 1 99 5 Dynamical solution of a model without energy barriers
In this note we study the dynamics of a model recently introduced by one of us, that displays glassy phenomena in absence of energy barriers. Using an adiabatic hypothesis we derive an equation for the evolution of the energy as a function of time that describes extremely well the glassy behaviour observed in Monte Carlo simulations.
متن کاملar X iv : c on d - m at / 9 30 70 65 v 1 2 9 Ju l 1 99 3 Chaos in short - range spin glasses
The nature of static chaos in spin glasses is studied. For the problem of chaos with magnetic field, scaling relations in the case of the SK model and short-range models are presented. Our results also suggest that if there is de Almeida-Thouless line then it is similar to that of mean-field theory for d = 4 and close to the h = 0 axis for d = 3. We estimate the lower critical dimension to be i...
متن کامل