The spectrum of 3d 3states Potts model and universality

1
The spectrum of 3d 3-statesPotts model and
universality

• Mario Gravina
• Univ. della Calabria INFN

collaborators R. Falcone, R.Fiore, A. Papa
SM FT 2006, Bari
2
OUTLINE
introduction
1) Svetitsky-Yaffe conjecture
2) Universal spectrum conjecture
3d 3q Potts model
numerical results
conclusions
SM FT 2006, Bari
3
Universality
1) SVETITSKY-YAFFE CONJECTURE
Theories with different microscopic interactions
but possessing the same underlying global
symmetry have common long-distance behaviour
finite temperature
if transition is 2nd order
what about 1st order phase transition?
SM FT 2006, Bari
4
2) universal mass spectrum
correlation function of
local order parameter
m1, m2, m3
SM FT 2006, Bari
5
universality conjecture
theory 1
theory 2
theory 3
Ising 3d
lF4 3d
SU(2) 4d
Fiore, Papa, Provero 2003
Caselle at al. 1999
Agostini at al. 1997






SM FT 2006, Bari
6
We want to test these two aspects of universality
3d 3q POTTS MODEL
L48
1) 1st order transition
L70
2) 3d Ising point
MONTE CARLO simulations
CLUSTER ALGORITHM
to reduce autocorrelation time
SM FT 2006, Bari
7
Potts model
Z(3) breaking
order-disorder PHASE TRANSITION
SM FT 2006, Bari
8
Phase diagram
Is the mass spectrum universal?
b
Z(3) broken phase
Does universality hold also for weak 1st order
transition?
comparison with SU(3) (work in progress)
bc
Falcone, Fiore, Gravina, Papa
Z(3) symmetric phase
h
hc
SM FT 2006, Bari
9
h0 1st order transition
order parameter is the magnetization
global spin
SM FT 2006, Bari
10
h0 1st order transition at finite volume
tunneling effects
0.5508
0.550565
complex M plane
SM FT 2006, Bari
11
h0 1st order transition at finite volume
To remove the tunneling between broken minima we
apply a rotation
only the real phase is present
SM FT 2006, Bari
12
Masses computation
MASS CHANNELS
by building suitable combinations of the local
variable
ZERO MOMENTUM PROJECTION
by summing over the y and z slices
VARIATIONAL METHOD
to well separate masses contributions in the same
channel
(Kronfeld 1990)
SM FT 2006, Bari
(Luscher, Wolff 1990)
13
0 CHANNEL
2 CHANNEL
b0.5508 h0
meff
m00.1556(36)
m20.381(17)
r
SM FT 2006, Bari
14
masses computation
1st order transition
m0
m2
0.60
n1/3
m0 (b1)0.1556
0.5508
b10.5508
0.550565
bt0.550565
b
0 channel
2 channel
in the scaling region
b2
SM FT 2006, Bari
0.550565 0.56 at least
15
mass ratio
prediction of 4d SU(3) pure gauge theory at
finite temperature screening mass ratio at finite
temperature?
b
SM FT 2006, Bari
16
2nd order Ising endpoint
Karsch, Stickan (2000)
ISING pt
(bc,hc) (0.54938(2),0.000775(10))
temperature-like
(tc,xc) (0.37182(2),0.25733(2))
ordering field-like
s_at_-r_at_-0.69
SM FT 2006, Bari
17
2nd order endpoint
0.37233
0.37248
SM FT 2006, Bari
18
local variable
Correlation function
order parameter
SM FT 2006, Bari
19
mass spectrum
right-pick
0 CHANNEL
2 CHANNEL
t0.37248 x0
We separated contributions from two picks and
calculated masses
m2
m0
0.0749(63)
0.188(12)
3d ISING VALUE
r
SM FT 2006, Bari
20
CONCLUSIONS
We used 3d 3q Potts model as a theoretical
laboratory to test some aspects of universality
THANK YOU
evidence found of universal spectrum
1) Ising point
2) weak 1st order tr. pt.
prediction of SU(3) screening spectrum?
left-pick?
SM FT 2006, Bari
21
SM FT 2006, Bari
22
1st order transition
weak
discontinous order parameter
the jump is small
SM FT 2006, Bari
23
Phase diagram
Mass spectrum is universal?
b
Z(3) broken phase
Universality also holds for weak 1st order
transition?
bc
Z(3) symmetric phase
h
hc
SM FT 2006, Bari
24
Universality
Critical exponents
order parameter
susceptibility
correlation lenght
SM FT 2006, Bari