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516
bio website unige.ch/math/folks/velenik
location Geneva, Switzerland
age 44
visits member for 2 years, 6 months
seen 3 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!


Apr
26
comment What happens to the free energy of the two-dimensional ising model with vortices?
I am not sure what you call vortices in the context of the Ising model (you can have them in continuous spin systems of course). What you can do (and maybe what you mean) is to force the presence of interfaces in the system. Forcing the presence of finitely many will not affect the (limiting) free energy density.
Apr
25
comment Ising model. What is large fluctuations of magnetization?
@Elias: if you have specific questions about our book, please do not hesitate to ask us directly (the relevant email address is given on the book page). For us, it is important to know what are the parts that should be clarified.
Mar
28
comment Symmetry Breaking And Phase transition
@Adam: But, stricto sensu, at the critical point, there is no transition from gas to liquid phases (the two are undistinguishable at that point). So, I keep with what I said: there is no symmetry breaking at the liquid/gas phase transition.
Mar
28
comment Symmetry Breaking And Phase transition
@Adam: But the question was "Is every phase transition associated with a symmetry breaking? If yes, what is the symmetry that a gaseous phase have but the liquid phase does not?", and the answer is negative.
Mar
28
comment Symmetry Breaking And Phase transition
@Adam: your argument does not apply to the first order phase transition between the liquid and gas phases, which I am discussing.
Mar
28
comment Symmetry Breaking And Phase transition
Note that it is easy to construct models with no symmetry in which 1st order phase transitions occur (actually this is the generic situation! You have to work harder to construct models with symmetry breaking). There is a mathematical theory devoted to this problem: the Pirogov-Sinai theory.
Mar
28
comment Symmetry Breaking And Phase transition
@Adam: It's just one rough model of the liquid/gas transition, and the symmetry is accidental. You can actually consider infinitely many perturbations of the Ising lattice gas, which we'll be just as good approximations to the real fluids, and in which there is no symmetry. There is no reason to expect that there is any, even hidden, symmetry for the real liquid/gas transition.
Mar
26
comment Symmetry Breaking And Phase transition
@Roopam : yes, of course they are not always related to symmetry breaking.
Mar
26
comment Symmetry Breaking And Phase transition
There is no symmetry breaking in the liquid/gas phase transition. As @Adam said, it is characterized by a jump in the density.
Mar
22
comment Pathria's “Statistical Mechanics” first edition
Yes, that's exactly what I mean. There are some well-known sites specialized in scanned copies of scientific books. I don't want to encourage piracy, of course, but it is sometimes very convenient when you want to have a quick look at the content and are too lazy to go to the library ;) (plus, you have the benefit of being able to electronically search through the text, which can be convenient if you're only looking for a particular statement that you expect might be in the book). I won't put a link here, but if you need one, write to me directly.
Mar
12
comment Pathria's “Statistical Mechanics” first edition
Any particular reason you're after the first edition? If it's to look at some specific part which has disappeared/been changed in later editions, then you might also simply try to find it online. It's very easy.
Mar
10
comment What is the resolution to Gibb's paradox?
I second the recommendation for Jaynes' beautiful paper . It can be found here: bayes.wustl.edu/etj/articles/gibbs.paradox.pdf .
Feb
28
comment How do we know that the Virial Expansion exists?
There are many proofs of convergence when the paremeters lie in suitable domains. See for example the classic book by Ruelle (I think that it's in Chapter 4): books.google.ch/books/about/… .
Jan
10
comment Divergent Series
A good place to start: terrytao.wordpress.com/2010/04/10/…
Jan
6
comment Probability of finding n particles in a volume v
I don't understand what you're trying to do in the second approach. How do you encode configurations? Just keeping track of how many of the $N$ particles are in $v$? If yes, then these are not equiprobable: just think of what happens when $v\ll V$; in that case, having all $N$ particles in $v$ has certainly not the same probability of having all of them in $V\setminus v$.
Dec
4
comment Physical intuition for independence of components of velocity in derivation of Maxwell–Boltzmann distribution
This assumption was actually the weakest point in Maxwell's derivations, as he fully realized himself. Indeed, in his subsequent paper "On the dynamical theory of heat" he found an alternative derivation avoiding this assumption. Later, Boltzmann further improved on these aspects in his paper "Studien über das Gleichgewicht der lebendigen Kraft zwischen bewegten materiellen Punkten".
Nov
28
comment Math needed for undergrad Statistical Mechanics/Thermal Physics
Well, it depends how far you want to go, but there is no way you can achieve a deep understanding of stat. mech. without having at least a reasonable understanding of probability theory...
Nov
20
comment Why isn't the 3 pts function vanishing in the Ising model by Z_2 symmetry?
If your computation is correct, yes, that seems to be the conclusion.
Nov
20
comment Why isn't the 3 pts function vanishing in the Ising model by Z_2 symmetry?
At zero external field, $n$-point functions with $n$ odd always vanish (when there is a unique infinite-volume Gibbs state, which is the case at the critical point). That's actually trivial if you start from the measure with free (or periodic) boundary conditions in a finite box, since then $\langle \sigma_i \sigma_j \sigma_k\rangle = -\langle (-\sigma_i) (-\sigma_j) (-\sigma_k)\rangle = -\langle \sigma_i \sigma_j \sigma_k\rangle$, by symmetry.
Nov
16
comment 2D Ising model simulations: Wolff algorithm acceptance probability with an external magnetic field
If the field is very close to zero, this should be ok. If not, then I don't see the point of using a cluster algorithm, just do spin flips.