1,537 reputation
516
bio website unige.ch/math/folks/velenik
location Geneva, Switzerland
age 44
visits member for 2 years, 4 months
seen 6 mins 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.


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
May
18
comment Question about the Boltzmann distribution
@yarnamc: Note that if the system $A$ is macroscopic, then the fluctuations of the energy density are extremely small. This is why the corresponding quantity in thermodynamics is considered deterministic.
May
15
comment What is the minimum non-integer dimension for which the XY model shows a phase transition? (if well-defined)
Of course, this universal behavior does not extend to $O(1)$: this is just the Ising model, which has a phase transition in dimension $2$ (and should have one for any dimension $d>1$, if you set up the model correctly). The difference is due to the fact that the symmetry of the latter is discrete, while it is continuous for $O(N)$ with $N\geq 2$.
May
14
comment What is the minimum non-integer dimension for which the XY model shows a phase transition? (if well-defined)
Depending how you set up your model in fractional dimensions, there will be long-range order as soon as $d>2$. The existence of long-range order is closely related to the transience of the random walk on the underlying graph. See this paper for one direction and this one for the other direction. Note that it is not clear how to make the latter paper rigorous, but it should be convincing for a theoretical physicist.
May
14
comment Is there anything physically infinite?
@user12345: Again, your statement "there is no physical law that we know of that would prevent a photon from travelling infinitely far" is about our current theories (it is a statement about a property of the set of physical laws we currently use to model physical reality), it is not about Nature. The only scientifically meaningful statements are those that can (at least in principle) be tested in experiments. Yours cannot.
May
13
comment Is there anything physically infinite?
That's obviously a correct statement. I don't understand how somebody can downvote this answer. Probably somebody clicking before thinking... not a very scientific attitude.
May
13
comment Is there anything physically infinite?
@user12345: I am only saying that such a statement is meaningless from an operational point of view (in that sense it's not science, but philosophy). Again, how would you test this hypothesis?
May
13
comment What is the interface tension between ordered and disordered phases of the Potts model?
Actually, I have no idea about that. Certainly, this must be completely open from a mathematical point of view. But I'd be surprised to hear that it's still a controversial issue for theoretical physicists (although what is known might depend on the geometry of the lattice)... I am sorry, but I really can't provide any information; my knowledge is limited to the mathematical aspects.
May
12
comment What is the interface tension between ordered and disordered phases of the Potts model?
@hlew: from the point of view of a mathematical physicist, there are plenty of open problems concerning the Potts model (including such basic ones as determining the order of the phase transition for the various values of the number of states and of the dimension). About what problem would still be considered open for a theoretical physicist, I unfortunately have no idea.
May
11
comment What is the interface tension between ordered and disordered phases of the Potts model?
@hlew: You're right. I should have checked ;) .
May
11
revised What is the interface tension between ordered and disordered phases of the Potts model?
Still more typos...
May
11
revised What is the interface tension between ordered and disordered phases of the Potts model?
Corrected a typo
May
11
comment Is there anything physically infinite?
These are infinities in our models of reality. Whether there exists anything actually infinite in Nature will belong forever to the realm of philosophy not physics (how would you devise an experiment to check the infinity of anything?).
May
11
answered What is the interface tension between ordered and disordered phases of the Potts model?
May
9
comment What is the interface tension between ordered and disordered phases of the Potts model?
I just realized that, in the title of your question, you are asking for the surface tension between the ordered and disordered states. The lack of symmetry between these two phases makes the definition slightly more involved than in the Ising case (or between 2 ordered Potts phases). Nevertheless, the idea remains completely similar, and you should first understand the definition in the link I have given. I can give you a more detailed explanation when symmetry is absent next week (I am at a conference right now...).
May
7
comment What is the interface tension between ordered and disordered phases of the Potts model?
The surface tension is defined as the surface-order contribution (per unit area) to the free energy coming from the presence of an interface between two phases. See scholarpedia.org/article/Interface_free_energy for example for a precise definition (in the Ising case, but the Potts case is essentially identical).
Apr
26
awarded  Yearling