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May
15
comment What is the length dimension in critical phenomena?
Hm, I had $\xi$ defined as $$\xi^2=\frac{\int_0^\infty r^2G(r)}{\int_0^\infty G(r)}$$ But anyway, I know the expression of the correlation function in the three regimes, I just fail to see why I should expect values that don't depend on the size of the system for dimensionless variables. Thank you for answering
May
15
comment What is the length dimension in critical phenomena?
@MengCheng I think it's the word length that confused me, sorry. For example the Binder cumulant as defined in the previous question ($\langle m^4\rangle/\langle m^2\rangle^2$) is dimensionless, why should it be better that $\xi/L$ to find the critical point?
May
15
comment What is the length dimension in critical phenomena?
@Danu Well, I know what a dimesionless variable is. I just don't know how that applies. If a quantity is dimensionless, then in a scale invariant system, it should not depend on size. Is that it? Why? And if so, should any dimensionless quantity I could build behave that way? For example, if the susceptibility goes like $\chi\sim L^{\gamma/\nu}$, then $\chi/L^{\gamma/\nu}$ behaves that way although it has dimensions.
May
15
asked What is the length dimension in critical phenomena?
May
15
comment How to interpret a null critical exponent?
@MengCheng Ok, thank you
May
15
comment How to interpret a null critical exponent?
And is there any deeper reason for it instead of being just because the $\log$ function diverges slower than any power?
May
15
asked How to interpret a null critical exponent?
May
9
answered Density of particles in hexagonal lattice
May
9
revised Density of particles in hexagonal lattice
edited title
May
9
asked Density of particles in hexagonal lattice
Apr
29
asked Sum in the reciprocal lattice
Feb
16
awarded  Organizer
Feb
16
revised Verification of mass density function in continuum mechanics
Added Latex for all formulae
Feb
16
suggested approved edit on Verification of mass density function in continuum mechanics
Feb
15
answered Does light itself experience time dilation?
Feb
7
awarded  Citizen Patrol
Feb
7
revised Lagrangian when there are gyroscopic effects
added 133 characters in body
Feb
6
asked Lagrangian when there are gyroscopic effects
Feb
4
comment How the torque/moment-of-force can be mathematically defined?
Yes it is, they are not being added, they are being multiplied. Do you have any trouble multiplying distance with the inverse of time to get a speed? This is the same thing.
Feb
4
comment How the torque/moment-of-force can be mathematically defined?
Well... you are not adding position and force which wouldn't make sense. You're multiplying them, which produces a new unit Newton*meter. Mathematically, they both belong to $\mathbb R^3$, so they belong to the same space and that product is perfetly well defined.