The definition of the word "mini" in the mobile phone world is constantly evolving. Take the LG G3 Beat, that was just leaked, which is one such "mini" phone; but it packs a 5" screen. To put this into perspective, the Nexus 5 has a 4.95" display; the Moto X, a 4.7" one.
The Beat, visually, looks like a slightly shrunken down LG G3; and even though it carries the "mini" moniker, there's certainly nothing subpar about the phone's specifications. The G3 Beat has 2GB RAM, 16GB internal storage with a microSD card slot, a quad-core 1.2GHz processor, 8MP camera, 4G LTE, a 2500mAh battery, and it runs on Android 4.4.2 out of the box.
The G3 Beat should be priced at around 2,500 yuan, which comes out to a little more than $400 SIM free. An official release date for the device hasn't been given, but don't expect it to be too far off from the G3's purported Mid-July release date.