Leeds Statistical Mechanics Discussion Group

Statistical Mechanics provides intriguing applications for, and connections between, many areas of Mathematics. This includes in particular (but is not limited to) areas of algebraic representation theory, combinatorics, dynamical/integrable systems, ergodic theory, stochastic processes, logic, analysis, and Probability currently studied here at Leeds. Accordingly we have a small informal study group investigating these connections.

To get the ball rolling, Jeanne Scott chaired initial meetings nominally explaining Potts models, partition functions, Tutte polynomials, matching polynomials and so on (and hoping to provoke participants into helping with any basic questions that arise). Paul has contributed this (draft) basic summary; and slides of several past review talks are linked below. Participants will be encouraged to contribute their own themes and connections for discussion.

All welcome.

Spring 11 session

We are holding regular weekly meetings this term discussing the topic of Quantum Computing.
Weekly (Chair: Rob): Fridays at 3pm in MALL 2. (Venues for March to be announced.)

Winter 10 session

42nd meeting: 1. Introduction/Welcome/Discussion (Chair: Rob) Nov. 5th (Friday) 3pm MALL 2
Alison's photo of the overview diagram.
Rob's suggested reading papers: 1, 2, 3, 4.
Paul's tentative suggested reading papers: try here (in particular the linked paper by Fendley and Krushkal).

43rd meeting: 1. Discussion (Chair: Rob) Nov. 12th (Friday) 3pm MALL 2

44th meeting: 1. Quantum Computing (Chair: Rob) Nov. 19th (Friday) 3pm MALL 2

45th meeting: 1. Quantum Computing II (Chair: Rob) Nov. 26th (Friday) 3pm MALL 2

46th meeting: 1. Quantum Computing III: Preskill, Chapter 2 (Chair: Rob) Dec. 3rd (Friday) 3pm MALL 2

LINKS: from Rob (Landsman's notes on Hilbert spaces)
from Matt (Preskill's more recent pages)

47th meeting: 1. Quantum Computing IV: Preskill, Chapter 2/3 (Chair: Abbas) Dec. 10th (Friday) 3pm MALL 2

Summer 10 session

39th meeting: Initial meeting for term: PROVISIONALLY April 29th (Thursday) 2pm Mall 1
*** Meeting POSTPONED for volcanic-ash-related reasons.
1. Introduction/Welcome/Discussion (Chair: Rob)

39th meeting: May 13th (Thursday) 2pm Mall 2
1. Paul Martin: "(Yang-Baxter equation and) The Solution of the 2D Ising model"

40th meeting: May 20th (Thursday) 2pm Mall 2
1. Paul Martin: "Solution of the 2D Ising model"
For those wishing to join at this point (!), page numbers 48-51 of this roughly cover what I did last time.

41st meeting: 1. Paul Martin: "Solution of the 2D Ising model (conclusion, at last)"

Spring 10 session

37th meeting: February 11th (Thursday) 2pm Mall 1
1. Introduction/Welcome/Discussion
2. Paul Martin: "Yang-Baxter equation and Statistical Mechanics"

38th meeting: March 11th (Thursday) 2pm Magic room
1. Paul Martin: "Toward the Solution of the 2D Ising model"

(39th meeting: postponed, twice!)

Winter 09 session

27th meeting: October 8th (Thursday) 3pm Mall 1
1. Introduction/Welcome/Discussion

28th meeting: October 9th (Friday) 3pm Mall 2
1. Andrew Reeves: "Statistical mechanics and the Temperley-Lieb algebras" (Notes to follow.)

29th meeting: October 16th (Friday) 3pm Mall 2
1. Andrew Reeves: "Statistical mechanics and Temperley-Lieb algebras II: 6-vertex model partition function (and possibly quantum groups)"

30th meeting: October 23th (Friday) 3pm Mall 2
1. Matt Daws: "Statistical mechanics and von Neumann algebras I"

31st meeting: October 30th (Friday) 3pm Roger Stevens Lecture Theatre 12
1. Matt Daws: "Statistical mechanics and von Neumann algebras II"

32nd meeting: November 6th (Friday) 3pm MALL 2
1. Rob Sturman: "Statistical mechanics, ergodic theory and Physics"

33rd meeting: November 13th (Friday) 3pm MALL 2
1. Rob Sturman: "Statistical mechanics, ergodic theory and Physics II"

34th meeting: November 20th (Friday) 3pm MALL 2
1. Rob Sturman: "Statistical mechanics, ergodic theory and Physics III"

35th meeting: December 4th (Friday) 3pm MALL 2
1. Matt Daws: "Statistical mechanics, von Neumann algebras and the Temperley-Lieb algebra"

36th meeting: December 11th (Friday) 3pm MALL 2
1. Matt Daws: "Statistical mechanics, von Neumann algebras and the Temperley-Lieb algebra II"

Subsequently: hopefully same coordinates weekly, but if need be the time can be changed. If you would like to be in the loop, drop us an email.

Previous meetings: Winter 08 session (including scans of participants' notes)
Previous meetings: Spring 09 session (including scans of participants' notes)
Previous meetings: Summer 09 session (including links for participants' notes)

Many thanks to Robert Marsh for the scanned notes so far. Copies of participants' notes of further meetings are being collated, and will be made available. Please contact Paul.

Links that have come up in discussions:

SMDG Emails that it might be helpful to broadcast: 
(Peter to Robert, on quivers in SM)
I have attached some stuff on the connections between quivers and 
Statistical Mechanics for Thursday. I hope some of its helpful ...

0011192v3 - is a handwaving way to define a quiver in Physics

0503149v2 - is a way of defining Statistical Mechanics from quivers

jehp122005025 - is an explicit quiver for the Ising model

0302228v1 - is formally why duals aren't very well defined ideas in
             (space+time) models of Physics. The mapping is known as
             "Wick-rotation", and to further confuse the issue, Physicists
             also interchange Euclidean-time with the temperature "beta"
             in this context.

0610003v2 - is a bit more what I'm doing on "time", using a description of 
9911114v1   the singularities associated with covering maps (space+time
             -> space) called asymptotic freedom.  


(Matt to Sathish, on temperature)
... (omitted -- hopefully Sathish's notes will abstract this)
All welcome

Organisers/Scientific Committee: Paul , Matt, Rob, Robert, Sathish, Jeanne