Monte Carlo calculation of the current-voltage characteristi(11)

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

derivativesofE1(r))beincludedsimplybyreplacingE1inEq.(15)by1/ (2

π/r )intheextremumequationI=E1/r .Ourrationaleforthischoiceisthatattheseparationr the

vortexpairisbrokenapartandwethereforeusethesti ness1/ (r)ofthesystematthis

separation.We ndtheappropriate (r)bysolvingselfconsistentlytheequation

I=1

(k )2π(19)

Theselfconsistent obtainedbysolvingEq.(19)willbedenoted .Therelationbetween

theexponenta(T)andthedielectricfunction isaccordingtoEqs.(15)and(10)givenby

theexpression(seeAmbegoakaretal.[17])

a(T)AHNS=1

T 2(21)

AsoneimmediatelyrealisesEq.(21)isnotconsistentwiththeactivationargumentused

toderiveEq.(20).InordertoreconcileEq.(21)witharateequationlikeEq.(13)

Minnhagenetal.havemadethefollowingsuggestion.Theyassumethattheactivationis

correctlyrepresentedbyΓinEq.(14).Therecombination,whichinEq.(13)isrepresented

1+bbytheinnocentlylookingtermn2F,isontheotherhandsupposedtobereplacedbynF

withb=2/(E1/T 2).Thesoleargumentforthisreplacementisunfortunatelysofar

simplytheobservationthatonethencanderiveEq.(21)fromanequationlikeEq.(13).

Nonetheless,weshallseebelowthatfortemperaturesbelowTcEq.(21) tsthesimulation

datamuchbetterthanEq.(20)does.Howeveramotivationforarecombinationterm

di erentfromtheoneinEq.(13)hasnotbeenpresented.AtTcbothrelationsreproduce

thesameexponenta(T=Tc)=2.