Re: [Phys-L] Spontaneous Symmetry Breaking in Unexpected Places: A Looped Double Catenary & A Block/Plank Balanced on a Cylinder (very long)

[David Bowman <David_Bowman@georgetowncollege.edu>]

Regarding JSD's musing:

> System [1] is particularly interesting, if I understand it rightly, because it is
> a second-order phase transition.
> There is a nontrivial relationship between Δ and σ in the slightly-broken
> regime. It might be amusing to plot this and to work out the critical
> exponent.

I've worked that out.  The 'order parameter' critical exponent has a classical mean-field value of 1/2.  In particular, if we let  Δ_0 =  0.257736456168094 be the critical mean relative excess slack, then just above the critical point the asymmetry parameter has the form, σ ≈ A*( Δ - Δ_0 )^(1/2).  I've also worked out a number of graphs for this system (including σ vs Δ).  I suppose I could post them somewhere if there is sufficient demand for them.

David Bowman