Alocal metallic state ingloballyinsulatingLa1.24Sr1.76Mn2O- well above themetalHinsulatortransitionZ.SUN1,2*J.F.DOUGLAS1.A.V.FEDOROV2,Y.-D.CHUANG2.H.ZHENG3,J.F.MITCHELL3ANDD.S.DESSAU1*NaturePhysics,Vol.3,p248(2007)Determination of theRegion of Existence of FerromagneticNanostructuresintheParaphaseofLa,-,Ba,MnO,bytheEPRMethodR.M.Eremina*,I.V.Yatsyk,Ya.M.Mukovskir,H.-A.Krug von Nidda, andA.LoidlISSN0021-3640,JETPLetters,2007,Vol.85,No.1,pp.51-54
ISSN 0021-3640, JETP Letters, 2007, Vol. 85, No. 1, pp. 51–54. Nature Physics, Vol. 3, p248 (2007)
Landau-GinzburgHamiltonianwithrandomtemperatureInordertodescribethephasetransitioninthequencheddisorderedsystemsLandau-GinzburgHamiltonianwithrandomtemperatureis usuallyusedH =[dDx(/V(x)P +(t+7(x)g2(x)+*(x)4T.(x)where , ang Ts(theto(El-criltica)) / T.(x)temperature.Its saddlepointequationisgivenby- 2d(x) +(t +t(x)d(x)+ gg3(x) = 0For thepuresystem,it isobvious that above Tc,thesaddlepoint solutioniszero.However in the earlystage of studyingthedisordered systems,itisstillassumed thatthe saddlepointsolutioniszero above Tc
Landau-Ginzburg Hamiltonian with random temperature In order to describe the phase transition in the quenched disordered systems, Landau-Ginzburg Hamiltonian with random temperature is usually used. ( )} 4 ( )) ( ) ~ ( 2 1 | ( ) | 2 1 { 2 2 4 x x x x g H d x t t D = + + + where , and is the local critical temperature. Its saddle point equation is given by ( ) ( ( ))/ ( ) ~ t + t x = T −Tc x Tc x (x) Tc ( )) ( ) ( ) 0 ~ ( ) ( 2 3 − x + t + t x x + g x = For the pure system, it is obvious that above Tc, the saddle point solution is zero. However in the early stage of studying the disordered systems, it is still assumed that the saddle point solution is zero above Tc
ReplicatrickConsiderthe short-range correlated disorder<t(x)T(y) >av= 8uo8(x -y)The probability of randomtemerperature is given byP((t(x))= CIlexp[-(t(x) /16uo]XThe averaged free energyis given by-βF =< ln z >an= [ P((T(x)))DT In([ Dpe-H)z"-1Using the identity equationIn z = limn-0nWe can get - βF =< ln z >a= lim(J Dp~ exp[-Her ]-1) / nTheeffective Hamiltonian is given byHer =JdDx(Z[/(x)P +t((x)* +g(b(x)*-uZ(ga(x)(p(x)3)α=l β=1Aweinrib andBIHalperin,Phys.Rev.B,27(1983)413
Replica trick Consider the short-range correlated disorder ( ) 8 ( ) ~ ( ) ~ t x t y av = u0 x − y ln( ) ~ ( )}) ~ ln ({ − − = = H a v F z P t x Dt De A weinrib and B I Halperin, Phys. Rev. B, 27 (1983) 413. ( )) /16 ] ~ ( )}) exp[ ( ~ ({ 0 2 P t x C t x u x = − The probability of random temerperature is given by The averaged free energy is given by Using the identity equation n z z n n 1 ln lim 0 − = → We can get F z D Heff n n a v ln lim ( exp[ ] 1)/ 0 − = = − − → = = = = + + − n n n D Heff d x t g u 1 1 2 2 0 2 2 4 1 ( ( )) ( ( )) ( ( )) ( ( )) ) 2 1 | ( )| 2 1 { [ x x x x x The effective Hamiltonian is given by
ReplicasymmetrybreakingIn1995,Dotsenkoet.alproposedthattheyshouldbenonzerosaddlepointsolutions abovethe critical temeprature.Considerthe saddlepoint equation- V2+(t +(x)+ g3 = 0For tthere dre some regions , where the seqsle<pointsolution can be nonzero. If the size of the region is lthe average ofreduced temperature is x olution is given byyr'(x) oc /-t(x)/g,T(x)<0There should be many isolated islands. Consider Auch isolated islands,There should be dlutionsNΦ~=;'(x),;=±1i=1V.S.Dotsenko,et al,J.Phys.A:Math.&Gen.,28 (1995)3093
There should be many isolated islands. Consider such isolated islands, There should be solutions For , there are some regions , where the saddle point solution can be nonzero. If the size of the region is , the average of reduced temperature is . The solution is given by Replica symmetry breaking ( )) 0 ~ ( 2 3 − + t + t x + g = In 1995, Dotsenko et. al proposed that they should be nonzero saddle point solutions above the critical temeprature. Consider the saddle point equation u0 t L0 ( ) 0 ~ ( )/ , ~ (x) − x g x i N N 2 ( ), 1 1 = = = i i N i i x V. S. Dotsenko, et al, J. Phys. A: Math. & Gen. , 28 (1995) 3093 ( ) 0 ~ t + t x ( ) ~ x