Suppose you have a field theory with a real scalar field $\phi$ and a potential term of the form $\lambda \phi^4 - \mu \phi^2$ that breaks the symmetry $\phi \to - \phi$ in the ground state. Is this symmetry restored in a scattering with high momentum transfer in any physically meaningful way? My problem is that there is no background field for which I could take a mean field approximation, so the usual argument for phase transitions does not work. 

One thing that came to my mind is that the potential will have higher order corrections, so maybe one could ask which way these corrections work in the limit $\Lambda \to \infty$, where $\Lambda$ is a UV scale? I know the first order correction for small $\phi$ does actually contribute to the breaking rather than to restoration, but then that doesn't seem to be the right limit for the scattering. If you don't know the answer I'd also be grateful for a reference. (Please do not point me to references that are for in-medium effects, nuclear matter etc, as I have plenty of these and it's not addressing my problem.)


Question: Is encrypting a single 128 bit block with AES ECB "safe"
Answer: Thomas' comment is correct.  While, theoretically, ECB is perfectly acceptable for use in a single block, the lack of any IV means your crypto system will leak information if you ever encrypt the same plaintext with the same key.  Even if you are encrypting discrete messages, I highly recommend using something that has an IV to prevent this kind of attack.

Though I don't know what application you are thinking of, in many cases when you are encrypting SSNs or similar, it may be worth using public/private key cryptography so as not to require having the private key anywhere on the machines that are accepting the input.