Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Phase diagram of simplified QCD

+ 4 like - 0 dislike
1159 views

Consider QCD with a single generation of massless quarks (u, d). This is probably the simplest variant of QCD which bears some relation to the real world. The theory has the following exact global symmetries:

  • U(1) acting on u and d (baryon number)
  • Chiral U(1) acting in opposite matter on left-hand and right-handed quarks. It is destroyed by an anomaly so we will not consider it further
  • SU(2) isospin rotation mixing u and d
  • Chiral SU(2). It is spontaneously broken
  • Charge conjugation C
  • Parity (spatial reflection) P
  • Time reversal T

A thermal equilibrium of the model is characterized by 3 parameters:

  • Temperature
  • Chemical potential associated to baryon number. Alternatively, baryon number density. We can use C to fix its sign
  • Chemical potential associated to isospin. Alternatively, isospin density. It is a vector but using isospin rotation symmetry we can align it along a prescribed axis, so we are left with a positive scalar parameter

Hence, the theory has a 3-dimensional phase diagram

How does the 3D phase diagram look like? Which phases do we have? Which phase transitions? What is the type of each phase transition?

Above a certain temperature T, chiral symmetry is restored. Btw, is this the same phase transition which breaks confinement? Above this T, we can introduce a 4th parameter, namely the chemical potential associated to chiral isospin. I suppose there a certain inequality governing the maximal value of this parameter as a function of the temperature?

How does the 4D phase diagram look like?

This post has been migrated from (A51.SE)
asked Nov 12, 2011 in Theoretical Physics by Squark (1,725 points) [ no revision ]
That's a huge research area, maybe you can narrow it down a bit.

This post has been migrated from (A51.SE)
Well, I would be content with a list of phases and phase transitions and a few words about each.

This post has been migrated from (A51.SE)

1 Answer

+ 4 like - 0 dislike

The situation is well represented in the following very pictorial picture

enter image description here

but this is a very active field of study. It is interesting to note that a real proof of existence for the critical endpoint (CEP, indicated as a critical point in the figure), both from a theoretical and numerical point of view, does not exist yet. The reason, at least for the lattice computations, arises from the infamous sign problem. When you discretize the action of the QCD with a chemical potential, this contribution becomes imaginary. So, several ways out have been devised but, as far as I can tell, none is taken for accepted widely. Finally, CEP is not really a critical point but a cross over point. This behaves as a true critical point for a phase transition if you take zero mass for quarks and zero chemical potential.

Note added: Just today appeared a paper by Owe Philipsen exactly on this matter (see here). The title is "Status of the QCD phase diagram from lattice calculations".

This post has been migrated from (A51.SE)
answered Nov 14, 2011 by JonLester (345 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
$\varnothing\hbar$ysicsOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...