Download presentation

Presentation is loading. Please wait.

Published byKylie Oliver Modified over 3 years ago

1
**The spectrum of 3d 3-states Potts model and universality**

Mario Gravina Univ. della Calabria & INFN collaborators: R. Falcone, R.Fiore, A. Papa SM & FT 2006, Bari

2
**OUTLINE introduction 3d 3q Potts model numerical results conclusions**

1) Svetitsky-Yaffe conjecture 2) Universal spectrum conjecture 3d 3q Potts model numerical results conclusions SM & FT 2006, Bari

3
**1) SVETITSKY-YAFFE CONJECTURE**

Universality 1) SVETITSKY-YAFFE CONJECTURE SU(N) d+1 confinement-deconfinement Theories with different microscopic interactions but possessing the same underlying global symmetry have common long-distance behaviour Z(N) d order-disorder finite temperature what about 1st order phase transition? if transition is 2nd order 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**

Ising 3d theory 1 theory 2 lF4 3d SU(2) 4d theory 3 Agostini at al. 1997 Caselle at al. 1999 Fiore, Papa, Provero 2003 m1 m2 m3 m4 m1 m2 m3 m4 m4 m1 m4 m1 m4 m1 = m1 m2 m3 m4 = m3 m1 m3 m1 m3 m1 = = m2 m1 m2 m1 m2 m1 = = SM & FT 2006, Bari

6
**We want to test these two aspects of universality**

3d 3q POTTS MODEL h b bc hc L=48 1) 1st order transition L=70 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 h=0 weak 1st order transition point**

Is the mass spectrum universal? 1st order critical lines 2nd order critical endpoint b Z(3) broken phase 2nd order critical ISING endpoint h=0 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
**h=0 – 1st order transition**

order parameter is the magnetization global spin SM & FT 2006, Bari

10
**h=0 – 1st order transition at finite volume**

tunneling effects 0.5508 between symmetric and broken phase between degenerated broken minima complex M plane SM & FT 2006, Bari

11
**h=0 – 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 b=0.5508 h=0 m0+=0.1556(36) m2+=0.381(17) meff r**

SM & FT 2006, Bari

14
**masses’ computation 1st order transition n=1/3 0+ channel 2+ channel**

0.60 m0+(b1) m0+(b2) n=1/3 m0+ (b1)=0.1556 0.5508 b1=0.5508 bt= b 0+ channel 2+ channel in the scaling region b2 SM & FT 2006, Bari – at least

15
mass ratio m2+ m0+ 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) h b bc hc z t Pc ISING pt h b bc hc temperature-like (bc,hc)= ( (2), (10)) (tc,xc)= ( (2), (2)) ordering field-like SM & FT 2006, Bari

17
2nd order endpoint SM & FT 2006, Bari

18
local variable Correlation function order parameter SM & FT 2006, Bari

19
**We separated contributions from two picks and calculated masses**

mass spectrum right-pick 0+ CHANNEL 2+ CHANNEL t= x=0 We separated contributions from two picks and calculated masses m0+ m2+ 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
**weak 1st order transition discontinous order parameter**

the jump is small Tt SM & FT 2006, Bari

23
**Phase diagram h=0 weak 1st order transition point**

Mass spectrum is universal? 1st order critical lines 2nd order critical endpoint b Z(3) broken phase 2nd order critical ISING endpoint h=0 Universality also holds for weak 1st order transition? bc Z(3) symmetric phase h hc SM & FT 2006, Bari

24
**Universality order parameter susceptibility correlation lenght**

Critical exponents Tc order parameter Tc susceptibility correlation lenght Tc SM & FT 2006, Bari

Similar presentations

OK

The Ising Model of Ferromagnetism by Lukasz Koscielski Chem 444 Fall 2006.

The Ising Model of Ferromagnetism by Lukasz Koscielski Chem 444 Fall 2006.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on new zealand culture past Ppt on power distribution grid Ppt on mpeg audio compression and decompression algorithms Conceptual architecture view ppt on android Ppt on index numbers youtube Ppt on event driven programming Free download ppt on the road not taken Ping pay ppt online Download ppt on home security system Ppt on business email etiquette