Monte Carlo calculation of the current-voltage characteristi(4)

We have studied the nonlinear current-voltage characteristic of a two dimensional lattice Coulomb gas by Monte Carlo simulation. We present three different determinations of the power-law exponent $a(T)$ of the nonlinear current-voltage characteristic, $V

Thepaperisorganizedasfollows:InSectionIIwede nethelatticeCoulombgas

model.InSectionIIIwestudyvariousapproachestotheIVcharacteristics.InSectionIV

wedescribeourMonteCarlomethodsforcalculatingIVcharacteristics.InSectionVwe

presenttheMonteCarloresults.SectionVIcontainsdiscussionandconclusions.

TTICECOULOMBGAS

Ausefulstartingpointforcalculationswithsuperconductorsinthepresenseofcurrents

and eldsistheGinsburg-Landaumodel,withtheorderparameterΨ(r)=|Ψ(r)|eiφ(r)

describingthesuperconductingorderofthesystem.However,thismodeldoesnotfocus

particularlyonvortexdegreesoffreedom.Thevorticesconstitutetheessentialdegreesof

freedomneartheKosterlitz-Thoulesstransition.AnapproximationtotheGinsburg-Landau

modelwhichfocusesonlyonthevorticesisgivenbytheCoulombgasmodel.Herethermal

uctuationsinthemagnitudeofΨareneglected,sincetheyarerelevantonlyclosetothe

mean- eldtransitiontemperature,whichisassumedtobewellabovethevortextransition

temperatureTc.Inoursimulationsthemodelisdiscretizedandputonalattice.The

approximationmadeinthelatticediscretizationwillonlya ecttheshortrangebehaviorof

thevortices,asthelatticede nesthesmallestpossibleseparation.Thecriticalproperties

willhowevernotbee ected.Ingeneral,largelengthscalepropertiesshouldbereasonable

modeledbythelatticeCoulombgasclosetoTc.

ThelatticeCoulombgas[14,15]isde nedbythepartitionfunctionZonasquarelattice

ofsidelengthLusingperiodicboundaryconditions:

Z=Trnexp[ β(H µN)]

H=1(1)