Calculate the absolute minimum difference between any two numbers in a huge array of integers

I have a very long array (300 000+ unsorted integers) in a Java program and need to calculate the smallest absolute difference between any two numbers within the array and display the absolute difference and the corresponding pair of numbers as output. The entire calculation should happen quickly.

I have the following code, which usually works:

private static void calcMinAbsDiff(int[] inputArray)
{
    Arrays.sort(inputArray);

    int minimum = Math.abs(inputArray[1] - inputArray[0]);

    int firstElement = inputArray[0];

    int secondElement = inputArray[1];

    for (int i = 2; i < inputArray.length; i++)
    {
        if(Math.abs(inputArray[i] - inputArray[i-1]) < minimum)
        {
            minimum = Math.abs(inputArray[i] - inputArray[i-1]);

            firstElement = inputArray[i-1];

            secondElement = inputArray[i];
        }
    }

    System.out.println("Minimum Absolute Difference : "+minimum);

    System.out.println("Pair of Elements : ("+firstElement+", "+secondElement+")");
}

However, the output I receive is all 0s. I believe this is because the array is too long.