  We present an argument to support the existence of dissipative modes in
relativistic field theories. In an O(N) $\varphi^4$ theory in spatial dimension
$d\le 3$, a relaxation constant $\Gamma$ of a two-point function in an infrared
region is shown to be finite within the two-particle irreducible (2PI)
framework at the next-leading order (NLO) of 1/N expansion. This immediately
implies that a slow dissipative mode with a dispersion $p_0\sim i\Gamma \p^2$
is microscopically identified in the two-point function. Contrary, NLO
calculation in the one-particle irreducible (1PI) framework fails to yield a
finite relaxation constant. Comparing the results in 1PI and 2PI frameworks,
one concludes that dissipation emerges from multiple scattering of a particle
with a heat bath, which is appropriately treated in the 2PI-NLO calculation
through the resummation of secular terms to improve long-time behavior of the
two-point function. Assuming that this slow dissipative mode survives at the
critical point, one can identify the dynamic critical exponent $z$ for the
two-point function as $z=2-\eta$. We also discuss possible improvement of the
result.
