Different symmetry realizations in relativistic coupled Bose systems at finite temperature and densities

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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
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Outline

• 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

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1- Motivation
The larger is the temperature, the larger is the
symmetry the smaller is the temperature, the
lesser is the symmetry
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Symmetry Breaking/Restoration in O(N) Scalar
Models
Relativistic case
Boundness
? unbroken - ? broken
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The potential V( ) for m2, N1 (Z2)
Lets heat it up!!
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Thermal Mass at high-T and N
M ²(N2)
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For ALL single field models
Higher order corrections do NOT alter this
pattern !!
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O(N)xO(N) Relativistic Models
(1974)
Boundness
?gt0 OR ?lt0!!
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Thermal masses to one loop
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Critical Temperatures at high-T and N2
M² (N2)
Transition patterns
Both m² lt 0 SR in the ? sector SNR in the
sector
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Transition patterns
M ²
Both m² gt 0 sector unbroken sector ISB
ISB
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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
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O(l T )
2
O(l T . l T/m )
Perturbation theory breaks down for temperatures
l T/m gt 1
Requires nonperturbation methods daisy and
superdaisy resum, Cornwall-Jackiw-Tomboulis
method, RG, large-N, epsilon-expansion, gap-equ
ations solutions, lattice, etc
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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)
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Conclusions for O(N)xO(N) relativistic ISB/SNR
are here to stay!! Applications?
Cosmology, eg, Monopoles/Domain Walls
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What happens in real condensed matter systems ?
(potassium sodium tartrate tetrahydrate)
Liquid crystals (SmC) ?Reentrant phase 383K lt T
lt 393K
Manganites (Pr,Ca,Sr)MnO , ?ferromagnetic
reentrant phase above the Curie temperature
(colossal magnetoresistence)
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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
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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
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Phase structure and the effective potential at
fixed charge
Z is evaluated in a systematic way
where
or
where
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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
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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
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Phase structure and the effective potential at
fixed charge
Minimizing the effective potential with respect
to µ
In the high density limit µ gtgt 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 gtgt m and high
temperature T
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Numerical Results (broken phase)
Charge increase - Symmetry never restored (SNR)
Small charge - Symmetry restored
PRD 44, 2480 (1991)
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Numerical Results (unbroken case)
Remember that
Ordinary ?0 have no Symmetry breaking
Unbroken case
But at high T and µ
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Numerical Results (unbroken case)
Broken symmetry at high T (ISB)
PRD 44, 2480 (1991)
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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
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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
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Thanks for your attention