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 (very draft update here) ; 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.

Winter '18 session

Fortnightly (Wednesday 14-15 approx, RVC): Topological QFT, loop braids and topological phases of matter.
main link here (Damiani - convenor)

Spring '17 session

Weekly (Thursday 10-12 approx, RVC): Towards topological phases, via higher gauge theory. (JFM convenor)

Spring '16 session

Weekly: Towards topological phases of matter. (ZK convenor)
(NB, May: Royce Zia (Virginia Tech) visiting and giving seminars on non-equilibrium stat mech...)
July Workshop: Modelling topological phases of matter

Autumn-Winter '15 session

Weekly: Towards topological phases of matter. (Read e.g. Hendryk Pfeiffer's Annals paper.)

Autumn-Winter '14 session

There are a lot of individual activities going on at the moment, so no time or need for the Group to run a separate meeting.
Here are some links:

Weekly (Tuesday 3-5 approx, PRD 9.305): When is a fusion category not a UMTC (or, why are 3d TQFTs so different; and where are the anyons)?
Wed 12th November, 2014 12:00 PM Richard A. Blythe (University of Edinburgh ) The evolution of combinatorial communication by natural selection
Friday 14th November, 2014 Roger Stevens 19, 4:00 PM Sid Redner (Santa Fe Institute and Department of Physics, Boston University) Fate of the Kinetic Ising and Potts Model
Wed 26th November, 2014 12:00 PM Samir Suweis (University of Padova (IT)) From Patterns to Principles: Statistical Physics of Ecological Networks

Winter '13 session

The plan is to address the theme: Knots and Statistical Mechanics
Please email specific suggestions to Rob or Paul.
We will start by noting that the TL category is a simple analogue (arising in Stat Mech) of the tangle category of knots, links and tangles; and that the PBR category is a generalisation of the TL category...

Nov 8th (Friday), 2pm, MALL2
1. PBR category I: Definitions (Chwas)

Nov 14th (Thursday), 2pm, MAGIC room
1. PBR category II: Algebras in low rank (Chwas)

Nov 15th (Friday), 1pm, MALL2
1. Welcome meeting , Open discussion and Intro to quasifree fermions (Chair: Zoltan)

Nov 21st (Thursday), 2pm, venue TBA
1. PBR category III (Chwas)

Dec 11th (Wednesday), 4pm, venue TBA
1. Fun with partition categories (Paul) (joint with ALA)

Spring/summer '13 session

Convenor: Rob

Feb 13th (Wednesday), 3-4pm, Maths Boardroom
1. Welcome meeting and Open discussion (Chair: Rob)   Alison's pic of the meeting: in Venn form!

Feb 20th (Wednesday), 4-5pm (NOTE CHANGE), venue Maths 8.22d
1. Open forum discussion (Chair: Rob)
2. TQFT I: Overview, Axioms and Applications (Zoltan and Paul) abstract

Feb 27th (Wednesday), 3-4pm (NOTE CHANGE), venue Maths RVC meeting room
1. Open forum discussion (Chair: Rob)
2. TQFT II: Axioms and Applications (Zoltan and Paul) abstract

March - May / Next few weeks: 1. Paul and Zoltan will be kicking around the subject "What the heck is a topological quantum field theory anyway?". Anyone who wants to join in should let Paul know. (Our nominal aim is to eventually say something about quantum computation; but Atiyah's and Feynman's original aims probably included things with stat mech connections, and we plan to start very broad, so this is fair game for SMDG.) Some reading: Kock's notes. Collateral reading: Karowski et al ; and see here ; ...

July 1-2, Zoltan's International Workshop, MALL1. Details here .

Further Topic Ideas for this session, and reading links:

2. Entropy and (classical) information...!
3. ...something like this ...!
1.+3. convergence maybe! Or... Yet more collateral reading: Coecke ; and here ; and more on this line also here .
4. Jarzynski's theorem (Mike)
5. Topological aspects of mixing (Rob)
6. ...

Spring/summer/winter 12 session

There will be some joint meetings with the QI group from Physics. See email circulation (let PPM know if you want to be added).
Reading: Kitaev's paper: 0901.2686 (on topological insulators via K-theory, Clifford algebras etc.)
Topological defects and K-theory: http://arxiv.org/abs/1006.0690
Majorana fermions (ref to follow)
Exception: May 17-18: go here instead! (ARTIN meeting in Leeds - several talks on themes we covered earlier.)

July 18th (Wednesday), 3-4 pm, E C Stoner SR 8.62
1. Peter Finch (Hannover, Germany) : "Spin and anyonic formulations for one-dimensional D3 and D(D3) models"

July 20th (Friday), 3-4 pm, EC Stoner Lab (10.72)
1. Benjamin Brown (Imperial College, London) : "Topological entanglement entropy with a Twist"

July 23rd (Monday) 14:00 MALL 1
1. Gavin Brennen (Sydney): "Low depth quantum circuits for Ising models"

July 25th (Wednesday) 12:15 QI Area (Physics)
1. Vaclav Zatloukal: "Transport properties of anyons in random topological environments"

See email circulation for abstracts.

Winter 11 session

Informal weekly meetings on ``Temperley-Lieb algebras and related problems in Stat Mech'' (Reeves' papers here: http://arxiv.org/abs/1111.0145 and http://arxiv.org/abs/1111.0146 ; connections with SM, QI and so on).
Weekly (chair: Paul): Fridays at 3pm in 9.18n (see email for variations).

Spring/summer 11 session

We are holding regular weekly meetings this semester discussing the topic of Quantum Computing (typically Preskill's notes - see below).
Weekly (Chair: Rob ): Fridays at 3pm in MALL 2.

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