1,829 reputation
1617
bio website unige.ch/math/folks/velenik
location Geneva, Switzerland
age 45
visits member for 3 years, 3 months
seen 25 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. Your feedback would be more than welcome!


2d
comment Simple mean-field “lattice gas” model
You can have a look at the discussion in Section 4.9, in chapter 4 here.
Jul
16
awarded  Fanatic
Jul
2
comment Random walk recurrence term and the self-energy
@DanielSank : if you want more detail on such computations, this is spelled out very explicitly in Chapter 7 here.
Jun
28
revised Phase transition without the Peierls' counter argument
Typos
Jun
24
revised Phase transition without the Peierls' counter argument
More precise
Jun
24
comment Phase transition without the Peierls' counter argument
@MathOverview: Peierls' argument is much more robust, as it only uses the spin-flip symmetry of the model (and even that can be removed, which leads to the powerful Pirogov-Sinai theory). Of course, the computation of the free energy provides a lot of additional information.
Jun
24
revised Phase transition without the Peierls' counter argument
added 470 characters in body
Jun
24
comment Phase transition without the Peierls' counter argument
@MathOverview: no Onsager's proof (or the many other approaches to the computation of the free energy) does not depend on the Peierls argument. It is an algebraic approach that does rely on very specific features of the Ising model. – Yvan Velenik just now
Jun
24
answered Phase transition without the Peierls' counter argument
Jun
24
comment Phase transition without the Peierls' counter argument
Onsager's computation implies the existence of a phase transition in dimension $2$ (for the nearest-neighbor model). Combined with correlation inequalities, this implies existence of a phase transition in any dimension $d\geq 2$, and interactions of any range (provided that nearest-neighbors also interact). So, yes, this is an alternative proof.
Jun
10
revised Can temperature be a complex number?
added 8 characters in body
Jun
10
answered Can temperature be a complex number?
Jun
10
awarded  Organizer
Jun
10
revised Transition from one state to another in Quantum Mechanics
Removed irrelevant tag
Jun
10
suggested approved edit on Transition from one state to another in Quantum Mechanics
Jun
4
comment Local and global detailed balance
Well, I am not sure about the physicists's terminology, but I guess that they refer to local detailed balance for the condition you wrote (it should be $k(x,y)\rho(x)=k(y,x)\rho(y)$ (for all $x$ and $y$), by the way), and to global detailed balance for the weaker condition $\sum_x \rho(x) k(x,y) = \rho(y)$ (for all $y$). In Markov chain theory, the latter characterizes the stationary distribution, while the former implies in addition that the Markov chain is reversible w.r.t. this distribution.
May
31
comment Is 'Boltzon' an accepted name for particles following Maxwell-Boltzmann (MB) statistics?
Some people also use Boltzmannons. There is no final consensus on this terminology.
May
28
comment What is normal fluctuation?
He probably means that the fluctuations of the relevant quantity (here the energy) follow a normal distribution. Actually, here he seems happy with the weaker claim that the scale of these fluctuations are of the right order (the variance is of order $N$).
May
13
comment Statistical Mechanics vs Statistics
First of all, the terminology statistical mechanics is rather unfortunate, and it would have been much better to call this theory probabilistic mechanics, for example. Indeed, the concepts and techniques of probability theory play an essential role in statistical mechanics (even if they are, quite wrongly, somewhat hidden in many books and courses). Statistics, however, is mostly irrelevant to statistical mechanics.
May
11
comment 1 dimensional Ising model
@Math_overview: Well, the way the Hamiltonian and free energy are defined here, the $\log 2$ term is fine. What makes you think this is incorrect if you agree with the computations?