1,879 reputation
1617
bio website unige.ch/math/folks/velenik
location Geneva, Switzerland
age 45
visits member for 3 years, 4 months
seen 6 hours ago

Professor at the Mathematics department of the University of Geneva. Mostly working at the intersection of probability theory and statistical physics.

With a colleague, we are in the process of writing an introductory book on the (classical) equilibrium statistical physics of lattice spin systems, from a mathematically rigorous point of view. A more detailed description of the project, as well as early drafts of several chapters can be found here. Your feedback would be more than welcome!


2d
comment Is the MaxEnt “interpretation” of statistical mechanics the current mainstream approach?
Sure, but a interpretation of probabilities in statistical mechanics is the core of any derivation of the latter. MaxEnt provides a subjective interpretation of the latter, the ergodicity/mixing approaches attempt (and fail) to provide a mechanical interpretation. I don't see how large deviations theory can be considered as an "alternative" approach to MaxEnt in this respect, as it has exactly nothing at all to say about this issue.
Aug
30
comment Is the MaxEnt “interpretation” of statistical mechanics the current mainstream approach?
I don't see what you mean by "getting the statistical physics framework based on the theory of large deviations". Large deviations theory, by definition, requires a probabilistic framework, which is precisely what is difficult to derive in an objective way from the underlying mechanical theory. The only thing that large deviations help you with is moving from one description (say, microcanonical) to another one (say, canonical). But you'd still need to derive the microcanonical probability measure in some way, and this is the hard part.
Aug
28
revised Reference for mathematics of statistical mechanics
Added a link
Aug
28
revised Reference for mathematics of statistical mechanics
Added a couple of additional references...
Aug
27
answered Reference for mathematics of statistical mechanics
Aug
13
comment Critical temperature and lattice size with the Wolff algorithm for 2d Ising model
@ACuriousMind: Done (but it is a bit sketchy, as I don't have so much time now; in particular, it would be nice to provide a picture of the specific heat for the 2d Ising model on a finite torus, as well as the limit quantity).
Aug
13
answered Critical temperature and lattice size with the Wolff algorithm for 2d Ising model
Aug
13
comment Critical temperature and lattice size with the Wolff algorithm for 2d Ising model
This is a well-understood finite-size effect, resulting from the fact that the correlation length in your system cannot become larger than the system size. It implies a shift of the (apparent) critical point of order $1/n$, if you're on an $n\times n$ torus. AFAIK, this was first studied by Ferdinand and Fisher in 1969 (Phys. Rev. 185, 832).
Aug
10
comment What are the definitions of microstates and macrostates?
They are in the same macrostate if they share the same values for the relevant set of macroscopic observables (which usually also imply that they share all macroscopic properties). They are in the same microsctate... well, if they share the same microscopic state.
Aug
5
comment Why does Landau theory not fail when dealing with a first order phase transition?
Yes, basically you have to assume the existence of a metastable branch of the free energy to "justify" the procedure. Note though that this assumption is simply wrong for short-range models (it can, for example, be proved rigorously that there is an essential singularity in the Ising model, in any dimension, which prevents analytic continuation of the free energy beyond the transition point).
Jul
27
comment Simple mean-field “lattice gas” model
You can have a look at the discussion in Section 4.9, in chapter 4 here.
Jul
16
awarded  Fanatic
Jul
2
comment Random walk recurrence term and the self-energy
@DanielSank : if you want more detail on such computations, this is spelled out very explicitly in Chapter 7 here.
Jun
28
revised Phase transition without the Peierls' counter argument
Typos
Jun
24
revised Phase transition without the Peierls' counter argument
More precise
Jun
24
comment Phase transition without the Peierls' counter argument
@MathOverview: Peierls' argument is much more robust, as it only uses the spin-flip symmetry of the model (and even that can be removed, which leads to the powerful Pirogov-Sinai theory). Of course, the computation of the free energy provides a lot of additional information.
Jun
24
revised Phase transition without the Peierls' counter argument
added 470 characters in body
Jun
24
comment Phase transition without the Peierls' counter argument
@MathOverview: no Onsager's proof (or the many other approaches to the computation of the free energy) does not depend on the Peierls argument. It is an algebraic approach that does rely on very specific features of the Ising model. – Yvan Velenik just now
Jun
24
answered Phase transition without the Peierls' counter argument
Jun
24
comment Phase transition without the Peierls' counter argument
Onsager's computation implies the existence of a phase transition in dimension $2$ (for the nearest-neighbor model). Combined with correlation inequalities, this implies existence of a phase transition in any dimension $d\geq 2$, and interactions of any range (provided that nearest-neighbors also interact). So, yes, this is an alternative proof.