1. DISTRIBUTED LATENT HEAT OF THE PHASE TRANSITIONS IN LOW-DIMENSIONAL CONDUCTORS V.Ya. Pokrovskii, Institute of Radioengineering and Electronics, Russian Academy of Sciences, Mokhovaya 11-7, Moscow, 125009, Russia Plan 1)The main idea. 2)What follows from it. 3)Comparison with experiments.

2. A classical 2nd-order phase transition: step of c p (or  ) Equivalent: K.H. Mueller, F. Pobell and Guenter Ahlers, Phys. Rev. Lett. 34, 513 (1975); “Phase Transition and Critical Phenomena”, edited by C. Domb and M.S. Green (Academic, New York, 1976), V. 6. V. Pasler, P. Schweiss, C. Meingast, B. Obst, H. Wuhl, A.I. Rykov and S. Tajima, Phys. Rev. Lett. 81, 1094 (1998). A classical 1st-order phase transition: Q=  H and a step-like change of dimensions  L x,y,z. Fluctuations: T c < T mf ; Typically, T mf – T c ~ T mf.

3. Usual description of the transitions: 3D-XY model (scaling): L. Onsager, Phys. Rev. 65, 117 (1944). -transition in He: K.H. Mueller, F. Pobell and Guenter Ahlers, Phys. Rev. Lett. 34, 513 (1975); “Phase Transition and Critical Phenomena”, edited by C. Domb and M.S. Green (Academic, New York, 1976), V. 6. Superconducting transition in layered compounds: V. Pasler, P. Schweiss, C. Meingast, B. Obst, H. Wuhl, A.I. Rykov and S. Tajima, Phys. Rev. Lett. 81, 1094 (1998). Peierls Transition: M.R. Hauser, B.B. Plapp, and G. Mozurkevich, Phys. Rev. B 43, 8105 (1991); J.W. Brill, M. Chung, Y.-K. Kuo, X. Zhan, E. Figueroa, and G. Mozurkewich, Phys. Rev. Lett 74, 1182 (1995); M. Chung, Y.-K. Kuo, X. Zhan, E. Figueroa, J.W. Brill, and G. Mozurkewich, Synth. Metals 71, 1891 (1995). Gaussian approach: Superconducting transition in layered compounds: C. Meingast, A. Junod, E. Walker, Physica C 272,106 (1996). Peierls Transition: M. Chung, Y.-K. Kuo, X. Zhan, E. Figueroa, J.W. Brill and G. Mozurkewich, Synth. Metals 71, 1891 (1995). Discontinuity at T c.

4. What is surprising: WHY not just shifting down?

6. Suppose, at |T-T c | >  T c /2 both c p and H follow MF, And for SOME reason  T c < T mf -T c.

7. What is surprising: WHY not just shifting down? Suppose, at |T-T c | >  T c /2 both c p and H follow MF, And for SOME reason  T c < T mf -T c. The only way: a smeared out STEP of H and MAXIMUM of c p. If  T c << T mf -T c, the maximum should dominate over the step.

8. Estimates. From the condition of the conservation of the area under c p (T) curve [C. Meingast, V. Pasler, P. Nagel, A. Rykov, S. Tajima, and P. Olsson, Phys. Rev. Lett. 86, 1606 (2001) ]: Integrating the maximum of c p (T) we can attribute a certain distributed latent heat to the transition (implying that c p =const for T c < T < T mf ).

9. How to check? T mf – only theoretically. K 0.3 MoO 3 [J.W. Brill, M. Chung, Y.-K. Kuo, X. Zhan, E. Figueroa, and G. Mozurkewich, Phys. Rev. Lett. 74, 1182 (1995); M. Chung, Y.-K. Kuo, X. Zhan, E. Figueroa, J.W. Brill, and G. Mozurkewich, Synth. Metals 71, 1891 (1995)] : 1) T mf - T c = 16 K from the CAS model [Z.Y. Chen, P.C. Albright, and J.V. Sengers, Phys. Rev. A 41, 3161 (1990).] 2)The width of the c p maximum is about 5 K. 3) The c p anomaly is about 2-3 times larger than the MF-step value (3 is not >>1, so both the step and the max. are seen)

10. The model of Gaussian fluctuations. The singular parts of c p above and below T c : [G. Mozurkewich, M.B. Salamon, S.E. Inderhees, Phys. Rev. B 46, 11914 (1992).] (t =|T-T c |/T c ) To avoid the divergency integrating we can cut off the anomaly at t=1 for (T mf - T c )/T c > 1 and at t=(T mf - T c )/T c for (T mf -T c )/T c < 1. - 1 st case - 2 nd case

11. The form of the c p (T) maximum? Particular model. We do not see a universal reason for  T c < T mf -T c. Approach from below: the precursor effect is the c p growth. We can attribute it to the nucleation of normal phase. Once T H c, and we can try to describe the whole transition region as thermal activation of the normal excitations: [V. Ya. Pokrovskii, A. V. Golovnya, and S. V. Zaitsev-Zotov, Phys. Rev. B 70, 113106 (2004).] Narrow transition: 1/W < 1/T c -1/T mf – collective excitations. No transition point?! No divergence – exponent.

12.  D. Starešinić et al., Eur. Phys. J. B 29, 71 ( 2002 ).  G. Mozurkewich et al., Synth. Met. 60, 137 ( 1993 ).

13. Not always: critical behavior is observed, e.g., for YBa 2 Cu 3 O x.  measurements demonstrate the tendency of evolution of a MF step into a wide maximum with the decrease of the doping (equivalent to the growth of anisotropy, and, consequently, of the 2D fluctuations) [C. Meingast, V. Pasler, P. Nagel, A. Rykov, S. Tajima, and P. Olsson, Phys. Rev. Lett. 86, 1606 (2001) ]  growth of T mf - T c. See also the tomorrow poster of A.V. Golovnya et al. Conclusions: 1.The simple consideration shows that a maximum of c p and  should be the prevailing effect observed at T c. 2.An estimate relating the distributed “latent heat” with the mean-field step of c p and the difference T mf -T c is given. 3.Agreement for c p (T) in K 0.3 MoO 3. Particular forms of c p (T) require particular models. 4.I am grateful to S.N. Artemenko, A.V. Golovnya, S.V. Zaitsev-Zotov, …