Minimization of lattice energy under fix box/relax

Dear all,
I have some perplexity about energy minimization for a periodic lattice.
I have several single element lattices:
-box size = size of the unit cell, with periodic BC applied
-lennard jones pair potential
-unit cell fcc with initial size that obtained by assuming atoms lie on the energy minimum of their nearest neighbour (initial nn distance = 2^1/6 * σ)

at this point the lattice is not at equilibrium because there are second, third and so on neigbour contributions that add additional attractive terms. I want to relax the lattice to its energy minimum at 0K
I was advised to use the energy minimization command combined with
fix 1 all box/relax iso 0.0 vmax 0.001 to let the box size vary in order to mantain the periodicity of the lattice consistently with the lattice parameter changing.

For this I have two questions:
1)how does that work? does that work because in an infinite periodic lattice at equilibrium any subportion must be unstrained and fix box/relax enforces that constraint?
2)the user manual specifies how minimization under fix box/relax is not well defined. Is there any more orthodox way of proceeding or should I restart the minimization until I achieve convergence?
Thank you,
Kind regards,

In a minimization (with fixed volume), the atoms follow the force to the (nearest) minimum. Since this is a high-dimensional problem, it is not possible to do an exhaustive search and if you have a rugged potential hyper-surface, you system may get trapped in local minima instead of the global minimum. If you start from an idealized geometry, this is less likely, since you have a lot of forces being canceled. If you add fix box/relax to that, the simulation cell is rescaled according to the computed pressure (and the corresponding target pressure). That can be done isotropically (in order to enforce maintaining symmetries) or anisotropically (adding more degrees of freedom that can enable minima otherwise not accessible, but also can lead to extra cost until the calculation converges). Also in this case it matters how smooth and well converged the potential hypersurface and pressure values are.

One alternate way I know about and that is particularly applicable to idealized geometries is to vary lattice settings and do a series of single point energy computations and then fit those values to an equation of state. This is used for quantum calculations, since there the computation is very expensive and getting an accurate and well converged pressure is particularly demanding and the EOS fit avoids that entirely.