Monte Carlo calculation of the current-voltage characteristi(17)

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

forT=0.24>Tcwesee,however,thatthereisnowellde nedlimitingsolutionfor as

j→0.ThisisbecausethesystemisabovetheKosterlitz-Thoulesstemperatureandvortex

pairswillalwaysdissociateirrespectiveofj.InFig.4thefunction isshownasafunctionoftemperature.Thesolidcirclesrepresent fromtheselfconsistentEq.(19)forthe xed

currentdensityj=0.03125.ThedatashownhererepresentstheconstructionshowninFig.

3.

Theresultsfromtheselfconsistentsolutionfor areanalyzedinFig.5.Herethe lled

circlesrepresenttheexponentaIV(T)fromFig.2.Theupsidedowntrianglesrepresent

aAHNS(T)fromEq.(20)withthesolutionfromFig.3andthetrianglesarethecorre-

spondingsolutiontoEq.(21).OnecanclearlyseethattheexpressioninEq.(21),derived

byMinnhagenetal.[21],reproducestheexponentaIV(T)forT<Tc.Notehowever,itis

onlyacoincidencethatEq.(20),derivedbyAmbegoakaretal.[17],worksfortemperatures

aboveTcinthis gureasthelimiting(j→0)solutionfor1/ isnotwellde nedforthese

temperatures,asalreadydiscussedinconnectionwithFig.3b.Asthesimulationdata

aIV(T)( lledcircles)alsomatchedtheexperimentaldatainFig.1wemustconcludethat

belowTctheinterpretationaccordingtoEq.(21)isclearlythemoreappropriate.

C.LinearResistance

Wewillnowturntoourlastdeterminationoftheexponenta(T).Theresultspresented

aboveallreliedonnon-equilibriumMonteCarlosimulations,i.e.witha niteapplied

supercurrentdensityj.Wewillnowpresenttheequilibriumdeterminationforj=0basedon

nitesizescalingofMonteCarlodataforthelinearresistancegivenbytheNyquistformula

(5)togetherwithEq.(17).InFig.6wedemonstrateadatacollapseofthelinearresistance

forseverallatticesizes.FromEq.(17)weseethatthelinearresistancedatacanbe

collapsedontoasinglecurve,thusrepresentingthethermodynamiclimit,byanappropriate

choiceateachtemperatureToftheexponentaR(T).Wedothisinthefollowingway.For

agiventemperaturewe ndtheexponentaRwhichminimizestheerrorofthe tde ned