Yvan Velenik

1,241 reputation

314

bio	website	unige.ch/math/folks/velenik
	location	Geneva, Switzerland
	age	43
visits	member for	1 year
	seen	11 hours ago
stats	profile views	94

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

	1,241 reputation	bio	website	unige.ch/math/folks/velenik	visits	member for	1 year
314 badges		location	Geneva, Switzerland		seen	11 hours ago

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20h	awarded	Citizen Patrol
2d	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
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