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

206 submissions , 164 unreviewed
5,103 questions , 2,249 unanswered
5,355 answers , 22,798 comments
1,470 users with positive rep
820 active unimported users
More ...

  Can Lee-Yang zeros theorem account for triple point phase transition?

+ 15 like - 0 dislike
623 views

Now the prominent Lee-Yang theorem (or Physical Review 87, 410, 1952) has almost become a standard ingredient of any comprehensive statistical mechanics textbook.

If the volume tends to infinity, some complex roots of the grand canonical partition function may converge to some points $z_0,z_1,z_2,\dots$ on the real axis. Thus these $\{ z_n \}$ divide the complex plane into some isolated phases. According to the singularity near the $\{z_n\}$ every two neighbouring phases may have phase transition phenomena occurring.

Here comes my question. Considering three phases surrounding a triple point in a phase diagram, they can transit to each other (just think about water). Since the neighbourhood along the real axis consists of only two possibilities, I wonder if this theory could account for a description of the triple point. And what is the connection between the neighbourhood of patches on the complex plane and the neighbourhood of phases in a phase diagram?


This post imported from StackExchange Physics at 2023-11-12 18:19 (UTC), posted by SE-user xiaohuamao

asked Nov 8, 2013 in Theoretical Physics by xiaohuamao (75 points) [ revision history ]
edited Nov 12, 2023 by Dilaton
If I remember correctly, the paper by Biskup et al, General Theory of Lee-Yang Zeros in Models with First-Order Phase Transitions, arXiv:math-ph/0004003, Phys. Rev. Lett. 84, 4794–4797 (2000), discusses, among others, the Blume-Capel model (which has a triple point).

This post imported from StackExchange Physics at 2023-11-12 18:19 (UTC), posted by SE-user Yvan Velenik
Note also that if you have three phases, you should consider two external fields.

This post imported from StackExchange Physics at 2023-11-12 18:19 (UTC), posted by SE-user Yvan Velenik

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:
p$\hbar$ysicsOverfl$\varnothing$w
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
...