dingping li school of physics, p eking university , china

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


Symmetry breaking pattern of vortex phase diagram.

replicatranslation

unbroken

unbroken

broken

broken

liquid

solid

Vortex glass

Bragg glass


Vortex glass

liquid

solidBragg Glass

structural (square-rhomb)

ODO

(melting

+s.p.)

Glass (irreversibility)


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

22

2 43 ( ) ( ) ( )2 2

2 1 ( ) 1 ( )F d x T Tc x xm

ie W x V xc

A

[ ] /( ) ( ) F TZ D x D x e

with variances

( ) ( ) ( ) ( )( ); ( )x y x yW W n x y V V q x y


Within the LLL approximation the gradient term is combined with the quadratic.

1/ 2

2 2 14 2

DT

t b G i t ba

2 / 3

3 14 2

DT

t b G i t ba

Therefore without disorder physical quantities depend on a single parameter:

Ruggeri, Thouless,1975


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) :

5.5spinodalTa

4.5Ta


9.5m

Ta

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, 2004.

13.2mTa

in 3D

in 2D

H

TT/Tc

T/TcCC

MM

5288.16 , 175.9 , 7.0 10c cT K H T Gi 2 3 7YBa Cu O Shibata et.al.,

PRB66,214518(02)


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”.


The unified order –disorder and Hx lines


65 70 75 80 85 90

5

10

15

20

25

30

2 3 7YBa Cu O

mH

xH

H

T*H

3D theoretical fitting of the optimally doped YBCO in DPL,BR, PRL90,167004(03)

Exp. inBouquet et al, Nature 414, 448 (2001)


Circles taken from Shibata et. al., PRB66, 214518 (02)

Triangles taken fromBouquet et al, Nature 414, 448 (2001)


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).


0 2 4 6 8 10 12

0

1

2

3

4

6 7 8 9 10 11

0

5

10

15

20

mH

gH

M MG

Shibauchi, PRB57, R5622 (1998)

2 2 - ( - ) [ ( ) ] kappa BEDT TTF Cu N CN Br

2D fitting of

Replica symmetry breaking line (or glass transition line) with small q

in 3D is given by4 / 3

1/ 3

3 4 5 43T

na n qn n

The glass transition line


xH liquid I to liquid II transition line. (black points – exp, pink - th)

60 65 70 75 80 85 90

5

10

15

20

25

30

Hupg

H lowg

H theg

mH

xHth

xH

The upper part of glass line of Shibata et.al., PRB66,214518(02) Hupg

H lowg

The low upper part of Taylor et alPRB68,054523 (03)

Phase diagram of optimally doped YBCO


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, PRL92,237004 (04) LaSCO


Fuchs et al PRL80,4911

(2002)

Sasagawa et al PRB61,1610 (00)

BSCCO LaSCO YBCO

Taylor et al PRB68,054523 (03)

Open question: glass line in solid


See our posters for details in

Theory (P56) and Experimental Fitting (P35)

dingping li school of physics, p eking university , china

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