Recent content by poiuyt

Homework Statement Consider the transverse field Ising model, with $$H=-J\sum_i\left(\sigma^x_i\sigma^x_{i+1}+g\sigma^z_i\right)$$ I have to calculate the magnetization $$\langle\sigma_z\rangle$$ at finite temperature. Homework EquationsThe Attempt at a Solution I have to say, I'm a bit lost.

Ok, one half gets F=pπr2 because the area is effectively just the one of the equator (right?). The force that holds together the two halves is the circle 2πr times the tension T. So you get p=2T/r. Then you have exactly the same calculation, but with a 2 instead of a 3: V = (Nkτ/2T)3/2(4π/3)-1/2...

maybe like this: dA/dV should go like 1/dr where r is the radius. If you do it for the whole balloon this is A/V=3/r. So effectively you get p = 3T/r = 3T (4π/3)1/3 V-1/3 then you plug this in the ideal gas law (I call the temperature τ) and you get pV=3T (4π/3)1/3 V-1/3 V = Nkτ and solving...

Homework Statement Take an elastic balloon of volume V in vacuum. The surface of the balloon has tension T. Find the pressure inside the balloon in terms of V and T, then combine this to the ideal gas law to find an expression for V. Homework Equations See below The Attempt at a Solution I...