1,517 reputation
516
bio website unige.ch/math/folks/velenik
location Geneva, Switzerland
age 44
visits member for 2 years, 4 months
seen 10 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.


Jul
1
awarded  Critic
Jun
18
comment The critical point of Bose-Hubbard model
There's no reason why the critical value should be computable, in general. Of course, it's probably possible to get some value through various approximations. Actually, you don't even specify the dimension, and the critical value will clearly depend on that information. If you mean 3 dimensions, then you have to realize that one does not even know how to compute the critical value in the 3d Ising model!
Jun
5
comment Partition function of a gas of $N$ identical classical particles
@fatema: Sorry, for some reason I wasn't notified of your comment/request. In case you're still looking for it: wase.urz.uni-magdeburg.de/~kassner/itp2/spezialseminar/… .
Jun
3
comment 1 dimensional Ising model
For the change of variables, the situation is similar: fixing the leftmost spin to be $+1$ has the advantage that the transformation from the $\sigma$ to the $\eta$ variables is invertible, otherwise we would have to keep the value of the original leftmost spin $\sigma_1$. I chose not to impose anything at the right end of the interval, since otherwise this would induce a constraint on the product of the $\eta$ spins.
Jun
3
comment 1 dimensional Ising model
@sreeram: in each case, I chose boundary conditions leading to simple computations. FOr example, in the case of low temperature expansion, imposing the $++$ boundary condition would add a constraint that the number of "domain walls" has to be even; of course, this can be done, but it makes the argument slightly less immediate. [TO BE CONTINUED]
Jun
2
comment 1 dimensional Ising model
@Vibert: What you said is correct, but only for the low temperature expansion. The high temperature expansion always gives rise to collections of edges, in any dimensions (well, at least as long as we only consider two-body interactions).
Jun
2
comment Is Brownian motion a deterministic system?
Yes, you can derive (in a suitable limit) the stochastic description of Brownian motion from the purely deterministic dynamics of hard spheres, see the following recent and quite remarkable paper: arxiv.org/abs/1305.3397 .
Jun
2
revised 1 dimensional Ising model
Minor corrections
Jun
1
comment Does a point exist in the real world
Also closely related to physics.stackexchange.com/questions/64197/… .
Jun
1
revised 1 dimensional Ising model
A couple of typo corrections and more precisions
Jun
1
comment 1 dimensional Ising model
Hopefully there aren't too many computational (or others) mistakes, as I had very little time to write this down... Don't hesitate to make corrections.
Jun
1
answered 1 dimensional Ising model
Jun
1
comment 1 dimensional Ising model
@sreeram: I don't know any, but I'll sketch an answer later if nobody does.
Jun
1
comment 1 dimensional Ising model
No, these expansions do apply in any dimensions. In dimension 1, they allow a simple computation of the free energy of the model, provided there is no magnetic field (otherwise the computations become more complicated than using the transfer matrix). This is also true of the change of variables method (which I assume refers to the change of variables $\eta_i = \sigma_i\sigma_{i+1}$ mapping the model to independent spins), which is only useful in dimension $1$.
May
23
revised Precise statement of Mermin–Wagner theorem
Added some information
May
23
revised Precise statement of Mermin–Wagner theorem
Added some references
May
23
comment Precise statement of Mermin–Wagner theorem
Not only is it not necessary to have isotropic coupling constants, but results even apply to a very large class of graphs (which can be extremely irregular). I'll add a couple of references in my post.
May
22
revised Precise statement of Mermin–Wagner theorem
One typo, and some clarifications
May
22
answered Precise statement of Mermin–Wagner theorem
May
20
awarded  Citizen Patrol