On the download page http://www.jetbrains.com/ruby/download/ it says:
Oracle JRE 1.6+ or OpenJDK 1.7+
On the knowledge base page, about a year old now, https://intellij-support.jetbrains.com/entries/23455956-Selecting-the-JDK-version-the-IDE-will-run-under under 'Linux' it says:
It's recommended that you will use the latest version of Oracle JDK 1.7 available for your system.
Using OpenJDK is not recommended, it has known visual and performance problems that affect some users.
Backstory and possibly helpful anecdote: OpenJDK 1.7 did NOT seem to work with the Ubuntu Unity Launcher. This is not the fault of RubyMine, it's probably Unity.
I encountered this documentation when searching for how to get the Rubymine Tools > Install Desktop Launcher menu item to work in Ubuntu 14.04 Unity desktop.
I had installed OpenJDK 1.7 java from the Ubuntu Software Center, where they only offer the OpenJDK. The Launcher would fail to start the program, probably logged somewhere.
To fix it, I ran uninstall of OpenJDK in Ubuntu Software Center, installed Oracle JDK1.8 from the advice here: http://www.webupd8.org/2012/09/install-oracle-java-8-in-ubuntu-via-ppa.html
sudo add-apt-repository ppa:webupd8team/java
sudo apt-get update
sudo apt-get install oracle-java8-installer
sudo apt-get install oracle-java8-set-default
and restart > Unity dash widget > RubyMine > right-click on launch bar menu item > Lock to launcher
It says you can easily switch your java8 for java7 by repeating the last commands and replace 8 with 7.
Next time I am going Mint with Cinnamon desktop!