9 votes

Why Curie temperature is bigger for smaller lattice in 2D Ising model

Why numerical simulation gives seemingly wrong result? The exact expression for $T_c$ is given by $$T_c=\frac{2J}{\ln\left(\sqrt{2}+1\right)}\approx 2.269\,J,$$ where we assume that $k_B=1$. This ...
Artem Alexandrov's user avatar
6 votes

Errors when the quantity is an exponent

The most general rule for uncertainty propagation comes from a derivative of the function. If you sketch a graph of a function, you can see how this works. For a function $f(x)$, if $\frac{\partial ...
Paul T.'s user avatar
  • 6,866
3 votes

Bar suspended by three vertical ropes

This is a canonical example of an underdefined problem (the number of unknowns (3 tensions) is less than the number of conditions (torque=0 and total force=0). You've tried to come up with a third ...
John's user avatar
  • 3,451
2 votes

Obtaining Geodesic equation for Massive particles using Schwarzschild metric

The second equation doesn't really come from the Euler-Lagrange equations (though one could probably derive it from them.) It's much easier to see from the definition of the particle's proper time: $$...
Michael Seifert's user avatar
1 vote

Pendulum equation

I am offering two ways of solving such question. The first method is the Lagrangian equation: $\frac{d}{dt}(\frac{\partial L}{\partial \dot q})=\frac{\partial L}{\partial q} \ and \ L= T-V$ where q ...
Laurens WU's user avatar
1 vote

How to correctly calculate minimum distance with kinematic equations

I think your answer is correct. An alternative approach, without calculus, is to note that the minimum separation will occur when the velocity of Q equals the constant velocity of P - up until this ...
gandalf61's user avatar
  • 47.4k
1 vote

Elongation of rod in two cases

Assuming Hooke's law holds in every case, what you said about case 1 is right. Assuming there is no friction, When only 1 force is applied to 1 end of the rod in case 2. Here the rod must be ...
Saif's user avatar
  • 33
1 vote

Potential - metal sphere in a uniform electric field

Yes, but your last equation is valid for all $\theta$. You can use this fact and the orthogonality of the Legendre polynomials to conclude that all the coefficients are zero. Indeed, for “any” ...
LPZ's user avatar
  • 9,525

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