Suppose your phone is not connected to any network. You are sitting in a cafeteria with 50 other people, everyone is communicating to each other via text messages. Is it possible through any device or way to capture messages within that field?
Yes. A Harris Stingray, Boeing DRT box, or other cell simulator can intercept SMS messages.
These are monitoring devices that have secretly been used by police agencies for over a decade. They come with strict non-disclosure agreements where the agencies that purchase them are not even allowed to acknowledge their existence to the public, and certainly are not available to the general public. As they have recently come into the sunlight, the legality of their use for warrantless wiretaps has been called into question. The state of California passed a law that took effect on 1 January, 2016, requiring officials to obtain a warrant to use them.
Researchers have used a cheap RTL-SDR receiver to decode SMS messages; be aware this would likely run afoul of various laws if applied to any messages but your own. If you're interested, here is a link to the project writeup.