Monte Carlo calculation of the current-voltage characteristi(10)

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

thanI theresistancewillbecuto bythe nitesizeLofthelatticeandtheresistance

becomesohmic.TheNyquistresistanceiscalculatedwithI=0andhence

R∝ 12T.(16)

ThismeansthatwecanscalethelinearresistanceRfromtheNyquistrelationEq.(5)withtheexponentE1/2T.Thisexponentispreciselya(T),theexponentofthenonlinear

IVcharacteristics(seeEq.(18)below),hence:

f(T)=RLa(T)(17)

shouldcollapseontoasinglecurvefordi erentlatticesizesL.I.e.f(T)shouldnotdepend

onlatticesizeL.Theresistanceweuseforthisscalingwillbetheonedeterminedfromthe

voltage uctuationsEq.(5).Theexponentdeterminedfromresistancedataatzerocurrent

willbedenotedaR(T).

C.NonlinearIVexponent

Wearegoingtomakeuseofacoupleofdi erentexpressionsforthepowerlawexpo-

nenta(T)ofthenonlinearIVcharacteristics.

characteristic:

V∝ E12TFromEq.(15)wegetthenonlinearIVI∝Ia(T)+1(18)

TheexponentcalculatedbymonitoringthevoltageresponseVasafunctionofanapplied

supercurrentIwillbedenotedaIV(T).Ona nitesystemwewillobtainanonlinearvoltage

responseonlyabovea niteappliedcurrent,givenbyI ～E1/L,suchthatthecurrentlength

r isshorterthanthesizeLofthesystem,asdiscussedabove.

D.SelfconsistentIVcharacteristic

AnotherexpressionfortheIVcharacteristicisobtainedifweincludetherdependence

inE1inEq.(10).Thelengthdependencecanina rstapproximation(inanexpansionin