1,517 reputation
516
bio website unige.ch/math/folks/velenik
location Geneva, Switzerland
age 44
visits member for 2 years, 3 months
seen 19 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.


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
Apr
23
comment Why does the Boltzmann factor $e^{-E/kT}$ seem to imply that lower energies are more likely?
No, the Boltzmann distribution is used for systems in contact with a reservoir, so the energy is not conserved. (Or, equivalently, for a finite subsystem of an isolated system; but in that case too, the Boltzmann factor takes into account the energy of the full subsystem and provides the probability density on the phase space of the subsystem.)
Apr
23
comment Why does the Boltzmann factor $e^{-E/kT}$ seem to imply that lower energies are more likely?
I don't think that restricting the Boltzmann factor to a specific degree of freedom is standard terminology (I just checked several books to see whether I had been misusing the term for years). The Boltzmann factor is usually seen as (say, in the classical case) the function $e^{-H/kT}$ on the phase space (where $H$ is the Hamiltonian of the system). It does provide the (unnormalized) probability density associated to the whole system.
Apr
16
awarded  Good Answer
Apr
9
comment Why there is no “Edison” unit in physics?
@Voitcus: This is not correct. His was the first able to play back a sound it previously recorded. The first sound recorder seems to be the Phonautograph, patented in 1857 by Édouard-Léon Scott de Martinville. Some of his recordings were played back in 2008. You can look it up, e.g., in wikipedia.
Apr
8
comment Does entropy really always increase (or stay the same)?
A nice discussion can be found at scholarpedia.org/article/… .
Mar
31
comment Is there a mechanism for time symmetry breaking?
You should read scholarpedia.org/article/… .
Mar
20
comment Results of Statistical Mechanics first obtained by formal mathematical methods
Actually, the opinion of XIXth Century physicists concerning the atomic theory is much more subtle than that. Interested people should read, e.g., the very nice books by Brush (The kind of motion we call heat, 2 volumes) and Cercignani (Ludwig Boltzmann:The Man Who Trusted Atoms).
Mar
20
revised Determining the probability of a particular site having a particular spin in an Ising model
More precise