1D Ising, the useless model for phase transitions

In my early studies on the melanins I was instructed to go and learn about phase transitions, since a knowledge of them is useful in understanding behaviour within materials in general. To start, I was given the 1D Ising model, which upon inspection was found to be a rather pathological system for studying phase transitions. The reason: it had none. This gave me some consternation as a wet behind the ears chemistry undergraduate trying to muscle into the physics department. Did I fail? What on earth was going on? Who would be so idiotic as to study this?
So, scraping together my courage I faced judgment day within the first 2 weeks of my honours project in front of my supervisor. However, after telling him my predicament, I was told that this was merely a test, and I passed. I felt pretty stoked, yet flustered for having made such a big deal out of it to myself.