Collaborators: R.L.S. Farias and R.O. Ramos

1. Different symmetry realizations in relativistic coupled Bose systems at finite temperature and densities Rodrigo Vartuli Department of Theoretical Physics,UERJ II Latin American Workshop on High Energy Phenomenology 5th December 2007 São Miguel das Missões, RS, Brazil Collaborators:R.L.S. Farias and R.O. Ramos

2. Motivation Study of symmetry breaking (SB) and symmetry restoration (SR) In multi-scalar field theories at finite T and are looking for the phenomena * symmetry nonrestoration (SR) * inverse symmetry breaking (ISB) How a nonzero charge affects the phase structure of a multi-scalar field theory? Work in progress and future applications Outline

3. 1- Motivation • The larger is the temperature, the larger is the symmetry • the smaller is the temperature, the lesser is the symmetry:

4. Symmetry Breaking/Restoration in O(N) Scalar Models Relativistic case: Boundness: +unbroken -broken

5. The potential V( ) for –m2, N=1 (Z2) Let´s heat it up!!

6. Thermal Mass at high-T and N M²(N=2)

7. For ALL single field models: Higher order corrections do NOT alter this pattern !!

8. O(N)xO(N) Relativistic Models (1974) Boundness: λ>0OR: λ<0!!

9. Thermal masses to one loop

10. Critical Temperatures at high-T and N=2 M² (N=2) Transition patterns Both m² < 0: SR in the ψ sector SNR in the sector

11. Transition patterns M ² Both m² > 0: sector: unbroken sector : ISB ISB

12. Temperature effects in multiscalar field models can change the symmetry aspects in unexpected ways: e.g. in the O(N)xO(N) example, it shows the possibilities of phenomena like inverse symmetry breaking (ISB) and symmetry nonrestoration (SNR) But be careful: Question: Can we trust perturbative methods at high temperatures ? NO ! (but these phenomena appear too in nonperturbative approaches)THEY ARE NOT DUE BROKEN OF PERTURBATION THEORY

13. 2 ~ O(l T ) 2 ~ O(l T . l T/m ) Perturbation theory breaks down for temperatures l T/m > 1 Requires nonperturbation methods: daisy and superdaisy resum, Cornwall-Jackiw-Tomboulis method, RG, large-N, epsilon-expansion, gap-equations solutions, lattice, etc

14. Nonperturbative methods are quite discordant about the occurrence or not of ISB/SNR phenomena: PLB 151, 260 (1985), PLB 157, 287 (1985), Z. Phys. C48, 505 (1990) Large-N expansion Gaussian eff potential PRD37, 413 (1988), Z. Phys. C43, 581 (1989) NO Chiral lagrangian method PRD59,025008 (1999) Bimonte et al NPB515, 345 (1998), PRL81, 750 (1998) Monte Carlo simulations PLB403, 309 (1997) Large-N expansion PLB366, 248 (1996), PLB388, 776 (1996), NPB476, 255 (1996) Gap equations solutions YES Renormalization Group PRD54, 2944 (1999), PLB367, 119 (1997) Bimonte et al NPB559, 103 (1999), Jansen and Laine PLB435, 166 (1998) Monte Carlo simulations Optimized PT (delta-exp) M.B. Pinto and ROR, PRD61, 125016 (2000)

15. Conclusions for O(N)xO(N) relativistic: ISB/SNR are here to stay!! Applications? Cosmology, eg, Monopoles/Domain Walls

16. What happens in real condensed matter systems ? (potassium sodium tartrate tetrahydrate) Liquid crystals (SmC*) Reentrant phase 383K < T < 393K Manganites: (Pr,Ca,Sr)MnO , ferromagnetic reentrant phase above the Curie temperature (colossal magnetoresistence) 3 Inverse melting (~ ISB) liquid  crystal: He3,He4, binary metallic alloys (Ti, Nb, Zr, Ta)  bcc to amorphous at high T Etc, etc, etc …. Review: cond-mat/0502033

17. Phase structure and the effective potential at fixed charge We start with the grand partition function Where H is the ordinary Hamiltonian and Using the standard manipulations like Legendre transformations … we get

18. Phase structure and the effective potential at fixed charge Z is evaluated in a systematic way where or where

19. Phase structure and the effective potential at fixed charge Using imaginary time formalism The renormalized effective potential in the high density and temperatures is given by where or PRD 44, 2480 (1991) Neglecting the zero point contribution similar made in

20. Phase structure and the effective potential at fixed charge The phase structure depends on the minima of the effective potential We have two minima: for unbroken symmetry and for broken symmetry

21. Phase structure and the effective potential at fixed charge Minimizing the effective potential with respect to µ In the high density limit µ >> m Now we will show numerical results for broken and unbroken phase of the theory with one complex scalar field Working at high density µ >> m and high temperature T

22. Numerical Results (broken phase) Charge increase - Symmetry never restored (SNR) Small charge - Symmetry restored PRD 44, 2480 (1991)

23. Numerical Results (unbroken case) Remember that Ordinary η=0 have no Symmetry breaking Unbroken case But at high T and µ

24. Numerical Results (unbroken case) Broken symmetry at high T (ISB) PRD 44, 2480 (1991)

25. In Preparation & For one complex scalar field we show very interesting results like (PRD 44, 2480 (1991)) • Symmetry non restoration • Inverse symmetry breaking & We are extending these calculations for two complex scalar fields

26. Future applications • Nonequilibrium dynamics of multi-scalar field • Theories • Markovian and • Non-Markovian evolutions for the fields… See poster: Langevin Simulations with Colored Noise and Non-Markovian Dissipation * In collaboration with L.A. da Silva R.L.S. Farias and R.O. Ramos

27. Thanks for your attention