I have read in many places that one point functions, like the one below:

$$\langle \Omega|\phi(x) |\Omega \rangle$$

are equal to zero (  $|\Omega \rangle$ is the vacuum of some interacting theory, $\phi$ is the field operator - scalar, spinorial, etc...)

Peskin's book, for instance, says (page 212) this is USUALLY zero by symmetry in the case of a scalar field ("usually" probably means $\lambda \phi^4$ theory) and by Lorentz invariance for higher spins . How can I see that?

In a more general question: can someone point out a counterexample? A case when this functions are not zero?

I have read in many places that one-point functions, like the one below:

$$\langle \Omega|\phi(x) |\Omega \rangle$$

are equal to zero ($|\Omega \rangle$ is the vacuum of some interacting theory, $\phi$ is the field operator - scalar, spinorial, etc...)

Peskin's book, for instance, says (page 212) this is USUALLY zero by symmetry in the case of a scalar field ("usually" probably means $\lambda \phi^4$ theory) and by Lorentz invariance for higher spins . How can I see that?

In a more general question: can someone point out a counterexample? A case when this functions are not zero?