IVW2005, TIFR, India Jan.11(2005)1 Dingping Li School of Physics, Peking University, China Baruch Rosenstein, NCTS&NCTU, Hsinchu, Taiwan, Weizmann Institute&Bar Ilan, Israel QUANTITATIVE THEORY OF THERMAL FLUCTUATIONS AND DISORDER IN THE VORTEX MATTER

IVW2005, TIFR, India Jan.11(2005)2 Symmetry breaking pattern of vortex phase diagram. replica translation unbroken broken liquid solid Vortex glass Bragg glass

IVW2005, TIFR, India Jan.11(2005)3 Vortex glass liquid solid Bragg Glass structural (square-rhomb) ODO (melting +s.p.) Glass (irreversibility)

IVW2005, TIFR, India Jan.11(2005)4 Thermal fluctuations are taken into account using the statistical sum with the GL energy in 2D (for simplicity) Ginzburg – Landau theory and the LLL approximation with variances

IVW2005, TIFR, India Jan.11(2005)5 Within the LLL approximation the gradient term is combined with the quadratic. Therefore without disorder physical quantities depend on a single parameter: Ruggeri, Thouless,1975

IVW2005, TIFR, India Jan.11(2005)6 Thermal fluctuations Vortex liquid 1. We constructed the Optimized gaussian series, which are convergent rather than asymptotic. Radius of convergence is Spinodal 2. Using gaussian approximation one finds that the solid becomes unstable at (spinodal). BR PRB60,4268 (1999) DPL, BR PRB65,024514(2001) Vortex Solid: 1. For the free energy we get to the required precision (.1%) at the two loop order (the IR divergencies due to “supersoft” phonons cancel exactly) :

IVW2005, TIFR, India Jan.11(2005)7 However it allowed us to verify unambiguously the validity of Borel- Pade method which provided a convergent scheme everywhere down to T=0. The melting is obtained by comparing liquid and solid free energy: DPL, BR, PRB, in 3D in 2D H T T/Tc Shibata et.al., PRB66,214518(02 )

IVW2005, TIFR, India Jan.11(2005)8 Point disorder, Unified ODO line, Kauzmann points 1. Disorder breaks the LLL scaling. Using perturbation around the zero disorder overcooled liquid and solid, we find that there is a single order – disorder line combining the melting line and the second peak line. Liquid gains more than solid from pinning and the line “curves down” at Kauzmann point in which the entropy jump vanishes. 2. The continuation of the “clean” melting line becomes a crossover (Hx) between liquid I and a viscous liquid II which we characterize as strongly correlated (deeply supercooled). Tricritical point is reinterpreted as a Kauzmann point. 3. In 3D the line has a “wiggle”.

IVW2005, TIFR, India Jan.11(2005)9 The unified order – disorder and Hx lines

IVW2005, TIFR, India Jan.11(2005)10 3D theoretical fitting of the optimally doped YBCO in DPL,BR, PRL90,167004(03) Exp. in Bouquet et al, Nature 414, 448 (2001)

IVW2005, TIFR, India Jan.11(2005)11 Circles taken from Shibata et. al., PRB66, (02) Triangles taken from Bouquet et al, Nature 414, 448 (2001)

IVW2005, TIFR, India Jan.11(2005)12 Replica symmetry breaking-Glass transition To calculate disorder averages we can use replica trick to integrate over disorder. Then we use the Mezard –Parisi Gaussian variational method to study the RSB. Lopatin Europhys. Let. 51,635 (00) DPL, BR, cond-mat (04), unpublished. Replica symmetry breaking solution means there is a hierarchy of relaxation times in dynamics (reflecting the logarithmically diverging energy barriers).

IVW2005, TIFR, India Jan.11(2005)13 Shibauchi, PRB57, R5622 (1998) 2D fitting of Replica symmetry breaking line (or glass transition line) with small q in 3D is given by The glass transition line

IVW2005, TIFR, India Jan.11(2005)14 liquid I to liquid II transition line. (black points – exp, pink - th) The upper part of glass line of Shibata et.al., PRB66,214518(02) The low upper part of Taylor et alPRB68, (03) Phase diagram of optimally doped YBCO

IVW2005, TIFR, India Jan.11(2005)15 Conclusion The LLL GL theory allows qualitative and quantitative comparison with experiment in a wide variety of type II materials in surprisingly wide range of fields and temperatures. It include the melting and the glass lines, in some cases magnetization and specific heat jumps and other quantities. The generic phase diagram contains four phases: liquid, solid, vortex glass and Bragg glass experimentally and theoretically in our approach. Divakar et al, PRL92, (04) LaSCO

IVW2005, TIFR, India Jan.11(2005)16 Fuchs et al PRL80,4911 (2002 ) Sasagawa et al PRB61,1610 (00) BSCCO LaSCO YBCO Taylor et al PRB68, (03) Open question: glass line in solid

IVW2005, TIFR, India Jan.11(2005)17 See our posters for details in Theory (P56) and Experimental Fitting (P35)